Edger: Differential Expression Analysis of Digital Gene

edgeR: diﬀerential expression analysis of digital gene expression data User’s Guide

Yunshun Chen, Davis McCarthy, Matthew Ritchie, Mark Robinson, Gordon K. Smyth

First edition 17 September 2008 Last revised 30 June 2016 Contents

1 Introduction 5 1.1 Scope ...... 5 1.2 Citation ...... 6 1.3 How to get help ...... 7 1.4 Quick start ...... 8

2 Overview of capabilities 9 2.1 Terminology ...... 9 2.2 Aligning reads to a genome ...... 9 2.3 Producing a table of read counts ...... 9 2.4 Reading the counts from a file ...... 10 2.5 The DGEList data class ...... 10 2.6 Filtering ...... 11 2.7 Normalization ...... 12 2.7.1 Normalization is only necessary for sample-specific effects ...... 12 2.7.2 Sequencing depth ...... 12 2.7.3 RNA composition ...... 12 2.7.4 GC content ...... 13 2.7.5 Gene length ...... 13 2.7.6 Model-based normalization, not transformation ...... 13 2.7.7 Pseudo-counts ...... 14 2.8 Negative binomial models ...... 14 2.8.1 Introduction ...... 14 2.8.2 Biological coefficient of variation (BCV) ...... 15 2.8.3 Estimating BCVs ...... 16 2.8.4 Quasi negative binomial ...... 17 2.9 Pairwise comparisons between two or more groups (classic) ...... 17 2.9.1 Estimating dispersions ...... 17 2.9.2 Testing for DE genes ...... 18 2.10 More complex experiments (glm functionality) ...... 19 2.10.1 Generalized linear models ...... 19

1 2.10.2 Estimating dispersions ...... 19 2.10.3 Testing for DE genes ...... 20 2.11 What to do if you have no replicates ...... 21 2.12 Diﬀerential expression above a fold-change threshold ...... 23 2.13 Gene ontology (GO) and pathway analysis ...... 24 2.14 Gene set testing ...... 25 2.15 Clustering, heatmaps etc ...... 25 2.16 Alternative splicing ...... 26 2.17 CRISPR-Cas9 and shRNA-seq screen analysis ...... 26

3 Specific experimental designs 28 3.1 Introduction ...... 28 3.2 Two or more groups ...... 28 3.2.1 Introduction ...... 28 3.2.2 Classic approach ...... 29 3.2.3 GLM approach ...... 30 3.2.4 Questions and contrasts ...... 31 3.2.5 A more traditional glm approach ...... 32 3.2.6 An ANOVA-like test for any differences ...... 33 3.3 Experiments with all combinations of multiple factors ...... 34 3.3.1 Defining each treatment combination as a group ...... 34 3.3.2 Nested interaction formulas ...... 36 3.3.3 Treatment effects over all times ...... 36 3.3.4 Interaction at any time ...... 37 3.4 Additive models and blocking ...... 37 3.4.1 Paired samples ...... 37 3.4.2 Blocking ...... 38 3.4.3 Batch effects ...... 40 3.5 Comparisons both between and within subjects ...... 40

4 Case studies 43 4.1 RNA-Seq of oral carcinomas vs matched normal tissue ...... 43 4.1.1 Introduction ...... 43 4.1.2 Reading in the data ...... 43 4.1.3 Annotation ...... 44 4.1.4 Filtering and normalization ...... 45 4.1.5 Data exploration ...... 46 4.1.6 The design matrix ...... 46 4.1.7 Estimating the dispersion ...... 47 4.1.8 Diﬀerential expression ...... 48 4.1.9 Gene ontology analysis ...... 50

2 4.1.10 Setup ...... 51 4.2 RNA-Seq of pathogen inoculated arabidopsis with batch effects ...... 52 4.2.1 Introduction ...... 52 4.2.2 RNA samples ...... 52 4.2.3 Loading the data ...... 52 4.2.4 Filtering and normalization ...... 53 4.2.5 Data exploration ...... 53 4.2.6 The design matrix ...... 54 4.2.7 Estimating the dispersion ...... 55 4.2.8 Differential expression ...... 56 4.2.9 Setup ...... 58 4.3 Profiles of Yoruba HapMap individuals ...... 59 4.3.1 Background ...... 59 4.3.2 Loading the data ...... 59 4.3.3 Filtering and normalization ...... 61 4.3.4 Estimating the dispersion ...... 62 4.3.5 Differential expression ...... 63 4.3.6 Gene set testing ...... 64 4.3.7 Setup ...... 66 4.4 RNA-Seq profiles of mouse mammary gland ...... 67 4.4.1 Introduction ...... 67 4.4.2 Read alignment and processing ...... 67 4.4.3 Count loading and annotation ...... 68 4.4.4 Filtering and normalization ...... 69 4.4.5 Data exploration ...... 70 4.4.6 The design matrix ...... 71 4.4.7 Estimating the dispersion ...... 72 4.4.8 Differential expression ...... 74 4.4.9 ANOVA-like testing ...... 76 4.4.10 Gene ontology analysis ...... 77 4.4.11 Gene set testing ...... 79 4.4.12 Setup ...... 80 4.5 Differential splicing after Pasilla knockdown ...... 81 4.5.1 Introduction ...... 81 4.5.2 RNA-Seq samples ...... 81 4.5.3 Read alignment and processing ...... 82 4.5.4 Count loading and annotation ...... 83 4.5.5 Filtering and normalization ...... 84 4.5.6 Data exploration ...... 85 4.5.7 The design matrix ...... 86 4.5.8 Estimating the dispersion ...... 86

3 4.5.9 Diﬀerential expression ...... 88 4.5.10 Alternative splicing ...... 88 4.5.11 Setup ...... 91 4.5.12 Acknowledgements ...... 91 4.6 CRISPR-Cas9 knockout screen analysis ...... 91 4.6.1 Introduction ...... 91 4.6.2 Sequence processing ...... 92 4.6.3 Filtering and data exploration ...... 92 4.6.4 The design matrix and dispersion estimation ...... 95 4.6.5 Diﬀerential representation analysis ...... 96 4.6.6 Gene set tests to summarize over multiple sgRNAs targeting the same gene ...... 98 4.6.7 Setup ...... 99 4.6.8 Acknowledgements ...... 100

4 Chapter 1

Introduction

1.1 Scope

This guide provides an overview of the Bioconductor package edgeR for differential expression analyses of read counts arising from RNA-Seq, SAGE or similar technologies [25]. The package can be applied to any technology that produces read counts for genomic features. Of particular interest are summaries of short reads from massively parallel sequencing technologies such as IlluminaTM, 454 or ABI SOLiD applied to RNA-Seq, SAGE-Seq or ChIP-Seq experiments and pooled shRNA-seq or CRISPR-Cas9 genetic screens. edgeR provides statistical routines for assessing differential expression in RNA-Seq experiments or differential marking in ChIP-Seq experiments. The package implements exact statistical methods for multigroup experiments developed by Robinson and Smyth [27, 28]. It also implements statistical methods based on generalized linear models (glms), suitable for multifactor experiments of any complexity, developed by McCarthy et al. [17], Lund et al. [15], Chen et al. [5] and Lun et al. [14]. Sometimes we refer to the former exact methods as classic edgeR, and the latter as glm edgeR. However the two sets of methods are complementary and can often be combined in the course of a data analysis. Most of the glm functions can be identified by the letters “glm” as part of the function name. The glm functions can test for differential expression using either likelihood ratio tests[17, 5] or quasi-likelihood F-tests [15, 14]. A particular feature of edgeR functionality, both classic and glm, are empirical Bayes methods that permit the estimation of gene-specific biological variation, even for experiments with minimal levels of biological replication. edgeR can be applied to differential expression at the gene, exon, transcript or tag level. In fact, read counts can be summarized by any genomic feature. edgeR analyses at the exon level are easily extended to detect differential splicing or isoform-specific differential expression. This guide begins with brief overview of some of the key capabilities of package, and then gives a number of fully worked case studies, from counts to lists of genes.

5 1.2 Citation

The edgeR package implements statistical methods from the following publications. Please try to cite the appropriate articles when you publish results obtained using the software, as such citation is the main means by which the authors receive credit for their work.

Robinson, MD, and Smyth, GK (2008). Small sample estimation of negative binomial dispersion, with applications to SAGE data. Biostatistics 9, 321–332.

Proposed the idea of sharing information between genes by estimating the negative binomial variance parameter globally across all genes. This made the use of negative binomial models practical for RNA-Seq and SAGE experiments with small to mod- erate numbers of replicates. Introduced the terminology dispersion for the variance parameter. Proposed conditional maximum likelihood for estimating the dispersion, assuming common dispersion across all genes. Developed an exact test for differential expression appropriate for the negative binomially distributed counts. Despite the of- ficial publication date, this was the first of the papers to be submitted and accepted for publication.

Robinson, MD, and Smyth, GK (2007). Moderated statistical tests for assessing diﬀerences in tag abundance. Bioinformatics 23, 2881–2887.

Introduced empirical Bayes moderated dispersion parameter estimation. This is a crucial improvement on the previous idea of estimating the dispersions from a global model, because it permits gene-speciﬁc dispersion estimation to be reliable even for small samples. Gene-speciﬁc dispersion estimation is necessary so that genes that behave consistently across replicates should rank more highly than genes that do not.

Robinson, MD, McCarthy, DJ, Smyth, GK (2010). edgeR: a Bioconductor package for diﬀerential expression analysis of digital gene expression data. Bioinformatics 26, 139–140.

Announcement of the edgeR software package. Introduced the terminology coeﬃcient of biological variation.

Robinson, MD, and Oshlack, A (2010). A scaling normalization method for diﬀerential expression analysis of RNA-seq data. Genome Biology 11, R25.

Introduced the idea of model-based scale normalization of RNA-Seq data. Proposed TMM normalization.

McCarthy, DJ, Chen, Y, Smyth, GK (2012). Diﬀerential expression analysis of multifactor RNA-Seq experiments with respect to biological variation. Nucleic Acids Research 40, 4288- 4297.

Extended negative binomial diﬀerential expression methods to glms, making the methods applicable to general experiments. Introduced the use of Cox-Reid approximate

6 conditional maximum likelihood for estimating the dispersion parameters, and used this for empirical Bayes moderation. Developed fast algorithms for ﬁtting glms to thousands of genes in parallel. Gives a more complete explanation of the concept of biological coeﬃcient of variation.

Lun, ATL, Chen, Y, and Smyth, GK (2016). It’s DE-licious: a recipe for diﬀerential expression analyses of RNA-seq experiments using quasi-likelihood methods in edgeR. Methods in Molecular Biology 1418, 391–416.

This book chapter explains the glmQLFit and glmQLFTest functions, which are al- ternatives to glmFit and glmLRT. They replace the chisquare approximation to the likelihood ratio statistic with a quasi-likelihood F-test, resulting in more conservative and rigorous type I error rate control.

Chen, Y, Lun, ATL, and Smyth, GK (2014). Diﬀerential expression analysis of complex RNA-seq experiments using edgeR. In: Statistical Analysis of Next Generation Sequence Data, Somnath Datta and Daniel S Nettleton (eds), Springer, New York.

This book chapter explains the estimateDisp function and the weighted likelihood empirical Bayes method.

Zhou X, Lindsay H, and Robinson MD (2014). Robustly detecting diﬀerential expression in RNA sequencing data using observation weights. Nucleic Acids Research, 42, e91.

Explains estimateGLMRobustDisp, which is designed to make the downstream tests done by glmLRT robust to outlier observations.

Dai, Z, Sheridan, JM, Gearing, LJ, Moore, DL, Su, S, Wormald, S, Wilcox, S, O’Connor, L, Dickins, RA, Blewitt, ME and Ritchie, ME (2014). edgeR: a versatile tool for the analysis of shRNA-seq and CRISPR-Cas9 genetic screens. F1000Research 3, 95.

This paper explains the processAmplicons function for obtaining counts from the fastq ﬁles of shRNA-seq and CRISPR-Cas9 genetic screens and outlines a general workﬂow for analyzing data from such screens.

1.3 How to get help

Most questions about edgeR will hopefully be answered by the documentation or references. If you’ve run into a question that isn’t addressed by the documentation, or you’ve found a conﬂict between the documentation and what the software does, then there is an active support community that can oﬀer help. The edgeR authors always appreciate receiving reports of bugs in the package functions or in the documentation. The same goes for well-considered suggestions for improvements. All other questions or problems concerning edgeR should be posted to the Bioconductor support

7 site https://support.bioconductor.org. Please send requests for general assistance and advice to the support site rather than to the individual authors. Posting questions to the Bioconductor support site has a number of advantages. First, the support site includes a community of experienced edgeR users who can answer most common questions. Second, the edgeR authors try hard to ensure that any user posting to Bioconductor receives assistance. Third, the support site allows others with the same sort of questions to gain from the answers. Users posting to the support site for the first time will find it helpful to read the posting guide at http://www.bioconductor.org/help/support/posting-guide. Note that each function in edgeR has its own online help page. For example, a detailed description of the arguments and output of the exactTest function can be read by typing ?exactTest or help(exactTest) at the R prompt. If you have a question about any particular function, reading the function’s help page will often answer the question very quickly. In any case, it is good etiquette to check the relevant help page first before posting a question to the support site. The authors do occasionally answer questions posted to other forums, such as SEQAn- swers or Biostar, but it is not possible to do this on a regular basis.

1.4 Quick start edgeR offers many variants on analyses. In general, the glm pipeline is recommended as it offers great flexibilities. There are two testing methods under the glm framework: likelihood ratio test and quasi-likelihood F-test. The details of these two methods are described in Chapter 2. A typical edgeR analysis might look like the following. Here we assume there are four RNA-Seq libraries in two groups, and the counts are stored in a tab-delimited text file, with gene symbols in a column called Symbol. > x <- read.delim("TableOfCounts.txt",row.names="Symbol") > group <- factor(c(1,1,2,2)) > y <- DGEList(counts=x,group=group) > y <- calcNormFactors(y) > design <- model.matrix(~group) > y <- estimateDisp(y,design) To perform quasi-likelihood F-tests: > fit <- glmQLFit(y,design) > qlf <- glmQLFTest(fit,coef=2) > topTags(qlf) To perform likelihood ratio tests: > fit <- glmFit(y,design) > lrt <- glmLRT(fit,coef=2) > topTags(lrt)

8 Chapter 2

Overview of capabilities

2.1 Terminology edgeR performs diﬀerential abundance analysis for pre-deﬁned genomic features. Although not strictly necessary, it usually desirable that these genomic features are non-overlapping. For simplicity, we will hence-forth refer to the genomic features as “genes”, although they could in principle be transcripts, exons, general genomic intervals or some other type of feature. For ChIP-seq experiments, abundance might relate to transcription factor binding or to histone mark occupancy, but we will henceforth refer to abundance as in terms of gene expression. In other words, the remainder of this guide will use terminology as for a gene-level analysis of an RNA-seq experiment, although the methodology is more widely applicable than that.

2.2 Aligning reads to a genome

The first step in an RNA-seq analysis is usually to align the raw sequence reads to a reference genome, although there are many variations on this process. Alignment needs to allow for the fact that reads may span multiple exons which may align to well separated locations on the genome. We find the subread-featureCounts pipeline [11, 12] to be very fast and effective for this purpose, but the Bowtie-TopHat-htseq pipeline is also very popular [1].

2.3 Producing a table of read counts edgeR works on a table of integer read counts, with rows corresponding to genes and columns to independent libraries. The counts represent the total number of reads aligning to each gene (or other genomic locus). Such counts can be produced from aligned reads by a variety of short read software tools. We ﬁnd the featureCounts function of the Rsubread package [12] to be particularly eﬀective

9 and convenient, but other tools are available such as findOverlaps in the GenomicRanges package or the Python software htseq-counts. Reads can be counted in a number of ways. When conducting gene-level analyses, the counts could be for reads mapping anywhere in the genomic span of the gene or the counts could be for exons only. We usually count reads that overlap any exon for the given gene, including the UTR as part of the ﬁrst exon [12]. For data from pooled shRNA-seq or CRISPR-Cas9 genetic screens, the processAmplicons function [7] can be used to obtain counts directly from fastq ﬁles. Note that edgeR is designed to work with actual read counts. We not recommend that predicted transcript abundances are input the edgeR in place of actual counts.

2.4 Reading the counts from a ﬁle

If the table of counts has been written to a file, then the first step in any analysis will usually be to read these counts into an R session. If the count data is contained in a single tab-delimited or comma-separated text file with multiple columns, one for each sample, then the simplest method is usually to read the file into R using one of the standard R read functions such as read.delim. See the quick start above, or the case study on LNCaP Cells, or the case study on oral carcinomas later in this guide for examples. If the counts for different samples are stored in separate files, then the files have to be read separately and collated together. The edgeR function readDGE is provided to do this. Files need to contain two columns, one for the counts and one for a gene identifier.

2.5 The DGEList data class edgeR stores data in a simple list-based data object called a DGEList. This type of object is easy to use because it can be manipulated like any list in R. The function readDGE makes a DGEList object directly. If the table of counts is already available as a matrix or a data.frame, x say, then a DGEList object can be made by

> y <- DGEList(counts=x)

A grouping factor can be added at the same time:

> group <- c(1,1,2,2) > y <- DGEList(counts=x, group=group)

The main components of an DGEList object are a matrix counts containing the integer counts, a data.frame samples containing information about the samples or libraries, and a optional data.frame genes containing annotation for the genes or genomic features. The data.frame samples contains a column lib.size for the library size or sequencing depth for

10 each sample. If not speciﬁed by the user, the library sizes will be computed from the column sums of the counts. For classic edgeR the data.frame samples must also contain a column group, identifying the group membership of each sample.

2.6 Filtering

Genes with very low counts across all libraries provide little evidence for differential expression. In the biological point of view, a gene must be expressed at some minimal level before it is likely to be translated into a protein or to be biologically important. In addition, the pronounced discreteness of these counts interferes with some of the statistical approxima- tions that are used later in the pipeline. These genes should be filtered out prior to further analysis. As a rule of thumb, genes are dropped if they can’t possibly be expressed in all the samples for any of the conditions. Users can set their own definition of genes being expressed. Usually a gene is required to have a count of 5-10 in a library to be considered expressed in that library. Users should also filter with count-per-million (CPM) rather than filtering on the counts directly, as the latter does not account for differences in library sizes between samples. Here is a simple example. Suppose the sample information of a DGEList object y is shown as follows:

> y$samples

group lib.size norm.factors Sample1 1 10880519 1 Sample2 1 9314747 1 Sample3 1 11959792 1 Sample4 2 7460595 1 Sample5 2 6714958 1

We ﬁlter out lowly expressed genes using the following commands:

> keep <- rowSums(cpm(y)>1) >= 2 > y <- y[keep, , keep.lib.sizes=FALSE]

Here, a CPM of 1 corresponds to a count of 6-7 in the smallest sample. A requirement for expression in two or more libraries is used as the minimum number of samples in each group is two. This ensures that a gene will be retained if it is only expressed in both samples in group 2. It is also recommended to recalculate the library sizes of the DGEList object after the ﬁltering though the diﬀerence is usually negligible.

11 2.7 Normalization

2.7.1 Normalization is only necessary for sample-specific effects edgeR is concerned with differential expression analysis rather than with the quantification of expression levels. It is concerned with relative changes in expression levels between conditions, but not directly with estimating absolute expression levels. This greatly simplifies the technical influences that need to be taken into account, because any technical factor that is unrelated to the experimental conditions should cancel out of any differential expression analysis. For example, read counts can generally be expected to be proportional to length as well as to expression for any transcript, but edgeR does not generally need to adjust for gene length because gene length has the same relative influence on the read counts for each RNA sample. For this reason, normalization issues arise only to the extent that technical factors have sample-specific effects.

2.7.2 Sequencing depth The most obvious technical factor that affects the read counts, other than gene expression levels, is the sequencing depth of each RNA sample. edgeR adjusts any differential expression analysis for varying sequencing depths as represented by differing library sizes. This is part of the basic modeling procedure and flows automatically into fold-change or p-value calculations. It is always present, and doesn’t require any user intervention.

2.7.3 RNA composition The second most important technical influence on differential expression is one that is less obvious. RNA-seq provides a measure of the relative abundance of each gene in each RNA sample, but does not provide any measure of the total RNA output on a per-cell basis. This commonly becomes important when a small number of genes are very highly expressed in one sample, but not in another. The highly expressed genes can consume a substantial proportion of the total library size, causing the remaining genes to be under-sampled in that sample. Unless this RNA composition effect is adjusted for, the remaining genes may falsely appear to be down-regulated in that sample [26]. The calcNormFactors function normalizes for RNA composition by finding a set of scaling factors for the library sizes that minimize the log-fold changes between the samples for most genes. The default method for computing these scale factors uses a trimmed mean of M- values (TMM) between each pair of samples [26]. We call the product of the original library size and the scaling factor the effective library size. The effective library size replaces the original library size in all downsteam analyses. TMM is the recommended for most RNA-Seq data where the majority (more than half) of the genes are believed not differentially expressed between any pair of the samples. The

12 following commands perform the TMM normalization and display the normalization factors.

> y <- calcNormFactors(y) > y$samples

group lib.size norm.factors Sample1 1 10880519 1.17 Sample2 1 9314747 0.86 Sample3 1 11959792 1.32 Sample4 2 7460595 0.91 Sample5 2 6714958 0.83

The normalization factors of all the libraries multiply to unity. A normalization factor below one indicates that a small number of high count genes are monopolizing the sequencing, causing the counts for other genes to be lower than would be usual given the library size. As a result, the library size will be scaled down, analogous to scaling the counts upwards in that library. Conversely, a factor above one scales up the library size, analogous to downscaling the counts.

2.7.4 GC content The GC-content of each gene does not change from sample to sample, so it can be expected to have little effect on differential expression analyses to a first approximation. Recent publications, however, have demonstrated that sample-specific effects for GC-content can be detected [24, 9]. The EDASeq [24] and cqn [9] packages estimate correction factors that adjust for sample-specific GC-content effects in a way that is compatible with edgeR. In each case, the observation-specific correction factors can be input into the glm functions of edgeR as an offset matrix.

2.7.5 Gene length Like GC-content, gene length does not change from sample to sample, so it can be expected to have little effect on differential expression analyses. Nevertheless, sample-specific effects for gene length have been detected [9], although the evidence is not as strong as for GC-content.

2.7.6 Model-based normalization, not transformation In edgeR, normalization takes the form of correction factors that enter into the statistical model. Such correction factors are usually computed internally by edgeR functions, but it is also possible for a user to supply them. The correction factors may take the form of scaling factors for the library sizes, such as computed by calcNormFactors, which are then used to compute the effective library sizes. Alternatively, gene-specific correction factors can be entered into the glm functions of edgeR as offsets. In the latter case, the offset matrix will

13 be assumed to account for all normalization issues, including sequencing depth and RNA composition. Note that normalization in edgeR is model-based, and the original read counts are not themselves transformed. This means that users should not transform the read counts in any way before inputing them to edgeR. For example, users should not enter RPKM or FPKM values to edgeR in place of read counts. Such quantities will prevent edgeR from correctly estimating the mean-variance relationship in the data, which is a crucial to the statistical strategies underlying edgeR. Similarly, users should not add artiﬁcial values to the counts before inputing them to edgeR. edgeR is not designed to work with estimated expression levels, for example as might be output by Cuﬄinks. edgeR can work with expected counts as output by RSEM, but raw counts are still preferred.

2.7.7 Pseudo-counts The classic edgeR functions estimateCommonDisp and exactTest produce a matrix of pseudo- counts as part of the output object. The pseudo-counts are used internally to speed up computation of the conditional likelihood used for dispersion estimation and exact tests in the classic edgeR pipeline. The pseudo-counts represent the equivalent counts would have been observed had the library sizes all been equal, assuming the fitted model. The pseudo-counts are computed for a specific purpose, and their computation depends on the experimental design as well as the library sizes, so users are advised not to interpret the psuedo-counts as general-purpose normalized counts. They are intended mainly for internal use in the edgeR pipeline. Disambiguation. Note that some other software packages use the term pseudo-count to mean something analogous to prior counts in edgeR, i.e., a starting value that is added to a zero count to avoid missing values when computing logarithms. In edgeR, a pseudo-count is a type of normalized count and a prior count is a starting value used to offset small counts.

2.8 Negative binomial models

2.8.1 Introduction The starting point for an RNA-Seq experiment is a set of n RNA samples, typically associated with a variety of treatment conditions. Each sample is sequenced, short reads are mapped to the appropriate genome, and the number of reads mapped to each genomic feature of interest is recorded. The number of reads from sample i mapped to gene g will be denoted ygi. The set of genewise counts for sample i makes up the expression proﬁle or library for that sample. The expected size of each count is the product of the library size and the relative abundance of that gene in that sample.

14 2.8.2 Biological coeﬃcient of variation (BCV)

RNA-Seq proﬁles are formed from n RNA samples. Let πgi be the fraction of all cDNA fragments in the ith sample that originate from√ gene g. Let G denote the total number of PG genes, so g=1 πgi = 1 for each sample. Let φg denote the coeﬃcient of variation (CV) (standard deviation divided by mean) of πgi between the replicates i. We denote the total number of mapped reads in library i by Ni and the number that map to the gth gene by ygi. Then E(ygi) = µgi = Niπgi.

Assuming that the count ygi follows a Poisson distribution for repeated sequencing runs of the same RNA sample, a well known formula for the variance of a mixture distribution implies: 2 var(ygi) = Eπ [var(y|π)] + varπ [E(y|π)] = µgi + φgµgi. 2 Dividing both sides by µgi gives

2 CV (ygi) = 1/µgi + φg.

The ﬁrst term 1/µgi is the squared CV for the Poisson distribution and the second is the squared CV of the unobserved expression values. The total CV2 therefore is the technical 2 2 CV with which πgi is measured plus the biological CV of the true πgi. In this article, we q call φg the dispersion and φg the biological CV although, strictly speaking, it captures all sources of the inter-library variation between replicates, including perhaps contributions from technical causes such as library preparation as well as true biological variation between samples. Two levels of variation can be distinguished in any RNA-Seq experiment. First, the relative abundance of each gene will vary between RNA samples, due mainly to biological causes. Second, there is measurement error, the uncertainty with which the abundance of each gene in each sample is estimated by the sequencing technology. If aliquots of the same RNA sample are sequenced, then the read counts for a particular gene should vary according to a Poisson law [16]. If sequencing variation is Poisson, then it can be shown that the squared coeﬃcient of variation (CV) of each count between biological replicate libraries is the sum of the squared CVs for technical and biological variation respectively,

Total CV2 = Technical CV2 + Biological CV2. Biological CV (BCV) is the coefficient of variation with which the (unknown) true abundance of the gene varies between replicate RNA samples. It represents the CV that would remain between biological replicates if sequencing depth could be increased indefinitely. The technical CV decreases as the size of the counts increases. BCV on the other hand does not. BCV is therefore likely to be the dominant source of uncertainty for high-count genes, so reliable estimation of BCV is crucial for realistic assessment of differential expression in

15 RNA-Seq experiments. If the abundance of each gene varies between replicate RNA samples in such a way that the genewise standard deviations are proportional to the genewise means, a commonly occurring property of measurements on physical quantities, then it is reasonable to suppose that BCV is approximately constant across genes. We allow however for the possibility that BCV might vary between genes and might also show a systematic trend with respect to gene expression or expected count. The magnitude of BCV is more important than the exact probabilistic law followed by the true gene abundances. For mathematical convenience, we assume that the true gene abundances follow a gamma distributional law between replicate RNA samples. This implies that the read counts follow a negative binomial probability law.

2.8.3 Estimating BCVs When a negative binomial model is fitted, we need to estimate the BCV(s) before we carry out the analysis. The BCV, as shown in the previous section, is the square root of the dispersion parameter under the negative binomial model. Hence, it is equivalent to estimating the dispersion(s) of the negative binomial model. The parallel nature of sequencing data allows some possibilities for borrowing information from the ensemble of genes which can assist in inference about each gene individually. The easiest way to share information between genes is to assume that all genes have the same mean-variance relationship, in other words, the dispersion is the same for all the genes [28]. An extension to this “common dispersion” approach is to put a mean-dependent trend on a parameter in the variance function, so that all genes with the same expected count have the same variance. However, the truth is that the gene expression levels have non-identical and dependent distribution between genes, which makes the above assumptions too naive. A more general approach that allows genewise variance functions with empirical Bayes shrinkage was introduced several years ago [27] and has recently been extended to generalized linear models and thus more complex experimental designs [17]. Only when using tagwise dispersion will genes that are consistent between replicates be ranked more highly than genes that are not. It has been seen in many RNA-Seq datasets that allowing gene-specific dispersion is necessary in order that differential expression is not driven by outliers. Therefore, the tagwise dispersions are strongly recommended in model fitting and testing for differential expression. In edgeR, we first estimate a common dispersion for all the tags and then apply an empirical Bayes strategy for squeezing the tagwise dispersions towards the common dispersion. The amount of shrinkage is determined by the prior weight given to the common dispersion (or the dispersion trend) and the precision of the tagwise estimates, and can be considered as the prior degrees of freedom. This prior degrees of freedom is estimated by examining the heteroskedasticity of the data [5].

16 2.8.4 Quasi negative binomial The NB model can be extended with quasi-likelihood (QL) methods to account for gene- speciﬁc variability from both biological and technical sources [15, 14]. Under the QL framework, the variance of the count ygi is a quadratic function of the mean,

2 2 var(ygi) = σg (µgi + φµgi),

2 where φ is the NB dispersion parameter and σg is the QL dispersion parameter. Any increase in the observed variance of ygi will be modelled by an increase in the esti- 2 mates for φ and/or σg . In this model, the NB dispersion φ is a global parameter whereas the QL is gene-specific, so the two dispersion parameters have different roles. The NB dispersion describes the overall biological variability across all genes. It represents the observed variation that is attributable to inherent variability in the biological system, in contrast to the Poisson variation from sequencing. The QL dispersion picks up any gene-specific variability above and below the overall level. The common NB dispersion for the entire data set can be used for the global parameter. In practice, we use the trended dispersions to account for the empirical mean-variance relationships. Since the NB dispersion under the QL framework reflects the overall biological variability, it does not make sense to use the tagwise dispersions. Estimation of the gene-specific QL dispersion is difficult as most RNA-seq data sets have limited numbers of replicates. This means that there is often little information to stably estimate the dispersion for each gene. To overcome this, an empirical Bayes (EB) approach is used whereby information is shared between genes [30, 15, 21]. Briefly, a mean-dependent trend is fitted to the raw QL dispersion estimates. The raw estimates are then squeezed towards this trend to obtain moderated EB estimates, which can be used in place of the raw values for downstream hypothesis testing. This EB strategy reduces the uncertainty of the estimates and improves testing power.

2.9 Pairwise comparisons between two or more groups (classic)

2.9.1 Estimating dispersions edgeR uses the quantile-adjusted conditional maximum likelihood (qCML) method for experiments with single factor. Compared against several other estimators (e.g. maximum likelihood estimator, Quasi- likelihood estimator etc.) using an extensive simulation study, qCML is the most reliable in terms of bias on a wide range of conditions and speciﬁcally performs best in the situation of many small samples with a common dispersion, the model which is applicable to Next- Gen sequencing data. We have deliberately focused on very small samples due to the fact

17 that DNA sequencing costs prevent large numbers of replicates for SAGE and RNA-seq experiments. The qCML method calculates the likelihood by conditioning on the total counts for each tag, and uses pseudo counts after adjusting for library sizes. Given a table of counts or a DGEList object, the qCML common dispersion and tagwise dispersions can be estimated using the estimateDisp() function. Alternatively, one can estimate the qCML common dispersion using the estimateCommonDisp() function, and then the qCML tagwise dispersions using the estimateTagwiseDisp() function. However, the qCML method is only applicable on datasets with a single factor design since it fails to take into account the eﬀects from multiple factors in a more complicated experiment. When an experiment has more than one factor involved, we need to seek a new way of estimating dispersions. Here is a simple example of estimating dispersions using the qCML method. Given a DGEList object y, we estimate the dispersions using the following commands. To estimate common dispersion and tagwise dispersions in one run (recommended): y <- estimateDisp(y) Alternatively, to estimate common dispersion: y <- estimateCommonDisp(y) Then to estimate tagwise dispersions: y <- estimateTagwiseDisp(y) Note that common dispersion needs to be estimated before estimating tagwise dispersions if they are estimated separately.

2.9.2 Testing for DE genes For all the Next-Gen squencing data analyses we consider here, people are most interested in finding differentially expressed genes/tags between two (or more) groups. Once negative binomial models are fitted and dispersion estimates are obtained, we can proceed with testing procedures for determining differential expression using the exact test. The exact test is based on the qCML methods. Knowing the conditional distribution for the sum of counts in a group, we can compute exact p-values by summing over all sums of counts that have a probability less than the probability under the null hypothesis of the observed sum of counts. The exact test for the negative binomial distribution has strong parallels with Fisher’s exact test. As we dicussed in the previous section, the exact test is only applicable to experiments with a single factor. The testing can be done by using the function exactTest(), and the function allows both common dispersion and tagwise dispersion approaches. For example: > et <- exactTest(y) > topTags(et)

18 2.10 More complex experiments (glm functionality)

2.10.1 Generalized linear models Generalized linear models (GLMs) are an extension of classical linear models to nonnormally distributed response data [20, 19]. GLMs specify probability distributions according to their mean-variance relationship, for example the quadratic mean-variance relationship speciﬁed above for read counts. Assuming that an estimate is available for φg, so the variance can be evaluated for any value of µgi, GLM theory can be used to ﬁt a log-linear model

T log µgi = xi βg + log Ni for each gene [13, 4]. Here xi is a vector of covariates that specifies the treatment conditions applied to RNA sample i, and βg is a vector of regression coefficients by which the covariate effects are mediated for gene g. The quadratic variance function specifies the negative binomial GLM distributional family. The use of the negative binomial distribution is equivalent to treating the πgi as gamma distributed.

2.10.2 Estimating dispersions For general experiments (with multiple factors), edgeR uses the Cox-Reid profile-adjusted likelihood (CR) method in estimating dispersions. The CR method is derived to overcome the limitations of the qCML method as mentioned above. It takes care of multiple factors by fitting generalized linear models (GLM) with a design matrix. The CR method is based on the idea of approximate conditional likelihood which reduces to residual maximum likelihood. Given a table counts or a DGEList object and the design matrix of the experiment, generalized linear models are fitted. This allows valid estimation of the dispersion, since all systematic sources of variation are accounted for. The CR method can be used to calculate a common dispersion for all the tags, trended dispersion depending on the tag abundance, or separate dispersions for individual tags. These can be done by calling the function estimateDisp() with a specified design. Alter- natively, one can estimate the common, trended and tagwise dispersions separately using estimateGLMCommonDisp(), estimateGLMTrendedDisp() and estimateGLMTagwiseDisp(), respectively. The tagwise dispersion approach is strongly recommended in multi-factor experiment cases. Here is a simple example of estimating dispersions using the GLM method. Given a DGEList object y and a design matrix, we estimate the dispersions using the following commands. To estimate common dispersion, trended dispersions and tagwise dispersions in one run (recommended): y <- estimateDisp(y, design)

19 Alternatively, one can use the following calling sequence to estimate them one by one. To estimate common dispersion: y <- estimateGLMCommonDisp(y, design)

To estimate trended dispersions: y <- estimateGLMTrendedDisp(y, design)

To estimate tagwise dispersions: y <- estimateGLMTagwiseDisp(y, design)

Note that we need to estimate either common dispersion or trended dispersions prior to the estimation of tagwise dispersions. When estimating tagwise dispersions, the empirical Bayes method is applied to squeeze tagwise dispersions towards common dispersion or trended dispersions, whichever exists. If both exist, the default is to use the trended dispersions. For more detailed examples, see the case study in section 4.1 (Tuch’s data), section 4.2 (arabidopsis data), section 4.3 (Nigerian data) and section 4.4 (Fu’s data).

2.10.3 Testing for DE genes For general experiments, once dispersion estimates are obtained and negative binomial models are fitted, we can proceed with testing procedures for determining differential expression using either the generalized linear model (GLM) likelihood ratio test or the quasi-likelihood (QL) F-test. The GLM likelihood ratio test is based on the idea of fitting negative binomial GLMs with the Cox-Reid dispersion estimates. The testing can be done by using the functions glmFit() and glmLRT(). Given raw counts, dispersion(s) and a design matrix, glmFit() fits the negative binomial GLM for each tag and produces an object of class DGEGLM with some new components. This DGEGLM object can then be passed to glmLRT() to carry out the likelihood ratio test. User can select one or more coefficients to drop from the full design matrix. This gives the null model against which the full model is compared using the likelihood ratio test. Tags can then be ranked in order of evidence for differential expression, based on the p-value computed for each tag. As a brief example, consider a situation in which are three treatment groups, each with two replicates, and the researcher wants to make pairwise comparisons between them. A generalized linear model representing the study design can be fitted to the data with commands such as:

> group <- factor(c(1,1,2,2,3,3)) > design <- model.matrix(~group) > fit <- glmFit(y, design)

20 The fit has three parameters. The first is the baseline level of group 1. The second and third are the 2 vs 1 and 3 vs 1 differences. To compare 2 vs 1:

> lrt.2vs1 <- glmLRT(fit, coef=2) > topTags(lrt.2vs1)

To compare 3 vs 1:

> lrt.3vs1 <- glmLRT(fit, coef=3)

To compare 3 vs 2:

> lrt.3vs2 <- glmLRT(fit, contrast=c(0,-1,1))

The contrast argument in this case requests a statistical test of the null hypothesis that coefficient3−coefficient2 is equal to zero. To find genes different between any of the three groups:

> lrt <- glmLRT(fit, coef=2:3) > topTags(lrt)

For more detailed examples, see the case study in section 4.1 (Tuch’s data) Alternatively, one can perform QL F-test to test for diﬀerential expression. While the likelihood ratio test is a more obvious choice for inferences with GLMs, the QL F-test is preferred as it reﬂects the uncertainty in estimating the dispersion for each gene. It provides more robust and reliable error rate control when the number of replicates is small. The QL dispersion estimation and hypothesis testing can be done by using the functions glmQLFit() and glmQLFTest(). To apply the QL method to the above example and compare 2 vs 1:

> fit <- glmQLFit(y, design) > qlf.2vs1 <- glmQLFTest(fit, coef=2) > topTags(qlf.2vs1)

Similarly for the other comparisons. For more detailed examples, see the case study in section 4.2 (arabidopsis data), section 4.3 (Nigerian data) and section 4.4 (Fu’s data).

2.11 What to do if you have no replicates edgeR is primarily intended for use with data including biological replication. Nevertheless, RNA-Seq and ChIP-Seq are still expensive technologies, so it sometimes happens that only one library can be created for each treatment condition. In these cases there are no replicate libraries from which to estimate biological variability. In this situation, the data analyst is faced with the following choices, none of which are ideal. We do not recommend any of

21 these choices as a satisfactory alternative for biological replication. Rather, they are the best that can be done at the analysis stage, and options 2–4 may be better than assuming that biological variability is absent.

1. Be satisﬁed with a descriptive analysis, that might include an MDS plot and an analysis of fold changes. Do not attempt a signiﬁcance analysis. This may be the best advice. 2. Simply pick a reasonable dispersion value, based on your experience with similar data, and use that for exactTest or glmFit. Typical values for the common BCV (square- root-dispersion) for datasets arising from well-controlled experiments are 0.4 for human data, 0.1 for data on genetically identical model organisms or 0.01 for technical replicates. Here is a toy example with simulated data:

> bcv <- 0.2 > counts <- matrix( rnbinom(40,size=1/bcv^2,mu=10), 20,2) > y <- DGEList(counts=counts, group=1:2) > et <- exactTest(y, dispersion=bcv^2) Note that the p-values obtained and the number of significant genes will be very sen- sitive to the dispersion value chosen, and be aware that less well controlled datasets, with unaccounted-for batch effects and so on, could have in reality much larger dispersions than are suggested here. Nevertheless, choosing a nominal dispersion value may be more realistic than ignoring biological variation entirely. 3. Remove one or more explanatory factors from the linear model in order to create some residual degrees of freedom. Ideally, this means removing the factors that are least important but, if there is only one factor and only two groups, this may mean removing the entire design matrix or reducing it to a single column for the intercept. If your experiment has several explanatory factors, you could remove the factor with smallest fold changes. If your experiment has several treatment conditions, you could try treating the two most similar conditions as replicates. Estimate the dispersion from this reduced model, then insert these dispersions into the data object containing the full design matrix, then proceed to model fitting and testing with glmFit and glmLRT. This approach will only be successful if the number of DE genes is relatively small. In conjunction with this reduced design matrix, you could try estimateGLMCommonDisp with method="deviance", robust=TRUE and subset=NULL. This is our current best attempt at an automatic method to estimate dispersion without replicates, although it will only give good results when the counts are not too small and the DE genes are a small proportion of the whole. Please understand that this is only our best attempt to return something useable. Reliable estimation of dispersion generally requires replicates. 4. If there exist a sizeable number of control transcripts that should not be DE, then the dispersion could be estimated from them. For example, suppose that housekeeping is

22 an index variable identifying housekeeping genes that do not respond to the treatment used in the experiment. First create a copy of the data object with only one treatment group:

> y1 <- y > y1$samples$group <- 1

Then estimate the dispersion from the housekeeping genes and all the libraries as one group:

> y0 <- estimateCommonDisp(y1[housekeeping,])

Then insert this into the full data object and proceed:

> y$common.dispersion <- y0$common.dispersion > et <- exactTest(y)

and so on. A reasonably large number of control transcripts is required, at least a few dozen and ideally hundreds.

2.12 Diﬀerential expression above a fold-change threshold

All the above testing methods identify differential expression based on statistical significance regardless of how small the difference might be. On the other hand, one might be more interested in studying genes of which the expression levels change by a certain amount. A commonly used approach is to conduct DE tests, apply a fold-change cut-off and then rank all the genes above that fold-change threshold by p-value. In some other cases genes are first chosen according to a p-value cut-off and then sorted by their fold-changes. These combinations of p-value and fold-change threshold criteria seem to give more biological meaningful sets of genes than using either of them alone. However, they are both ad hoc and do not give meaningful p-values for testing differential expressions relative to a fold-change threshold. They favour lowly expressed but highly variable genes and destroy the control of FDR in general. edgeR offers a rigorous statistical test for thresholded hypotheses under the GLM framework. It is analogous to TREAT [18] but much more powerful than the original TREAT method. Given a fold-change (or log-fold-change) threshold, the thresholded testing can be done by calling the function glmTreat() on a DGEGLM object produced by either glmFit() or glmQLFit(). In the example shown in section 2.10.3, suppose we are detecting genes of which the log2-fold-changes for 1 vs 2 are significantly greater than 1, i.e., fold-changes significantly greater than 2, we use the following commands:

23 > fit <- glmFit(y, design) > tr <- glmTreat(fit, coef=2, lfc=1) > topTags(tr)

Note that the fold-change threshold in glmTreat() is not the minimum value of the fold- change expected to see from the testing results. Genes will need to exceed this threshold by some way before being declared statistically signiﬁcant. It is better to interpret the threshold as “the fold-change below which we are deﬁnitely not interested in the gene” rather than “the fold-change above which we are interested in the gene”. In the presence of a huge number of DE genes, a relatively large fold-change threshold may be appropriate to narrow down the search to genes of interest. In the lack of DE genes, on the other hand, a small or even no fold-change threshold shall be used. For more detailed examples, see the case study in section 4.4 (Fu’s data).

2.13 Gene ontology (GO) and pathway analysis

The gene ontology (GO) enrichment analysis and the KEGG pathway enrichment analysis are the common downstream procedures to interpret the differential expression results in a biological context. Given a set of genes that are up- or down-regulated under a certain contrast of interest, a GO (or pathway) enrichment analysis will find which GO terms (or pathways) are over- or under-represented using annotations for the genes in that set. The GO analysis can be performed using the goana() function in edgeR. The KEGG pathway analysis can be performed using the kegga() function in edgeR. Both goana() and kegga() take a DGELRT or DGEExact object. They both use the NCBI RefSeq annotation. Therefore, the Entrez Gene identifier (ID) should be supplied for each gene as the row names of the input object. Also users should set species according to the organism being studied. The top set of most enriched GO terms can be viewed with the topGO() function, and the top set of most enriched KEGG pathways can be viewed with the topKEGG() function. Suppose we want to identify GO terms and KEGG pathways that are over-represented in group 1 compared to group 2 from the previous example in section 2.10.3 assuming the samples are collected from mice. We use the following commands:

> qlf <- glmQLFTest(fit, coef=2) > go <- goana(qlf, species="Mm") > topGO(go) > keg <- kegga(qlf, species="Mm") > topKEGG(keg)

For more detailed examples, see the case study in section 4.1 (Tuch’s data) and section 4.4 (Fu’s data).

24 2.14 Gene set testing

In addition to the GO and pathway analysis, edgeR offers different types of gene set tests for RNA-Seq data. These gene set tests are the extensions of the original gene set tests in limma in order to handle DGEList objects. The roast() function performs ROAST gene set tests [33]. It is a self-contained gene set test. Given a gene set, it tests whether the majority of the genes in the set are DE across the comparison of interest. The mroast() function does ROAST tests for multiple sets, including adjustment for multiple testing. The fry() function is a fast version of mroast(). It assumes all the genes in a set have equal variances. Since edgeR uses the z-score equivalents of NB random deviates for the gene set tests, the above assumption is always met. Hence, fry() is recommended over roast() and mroast() in edgeR. It gives the same result as mroast() with an infinite number of rotations. The camera() function performs a competitive gene set test accounting for inter-gene correlation. It tests whether a set of genes is highly ranked relative to other genes in terms of differential expression [34]. The romer() function performs a gene set enrichment analysis. It implements a GSEA approach [31] based on rotation instead of permutation. Unlike goana() and kegga(), the gene set tests are not limited to GO terms or KEGG pathways. Any pre-defined gene set can be used, for example MSigDB gene sets. A common application is to use a set of DE genes that was defined from an analysis of an independent data set. For more detailed examples, see the case study in section 4.3 (Nigerian’s data) and section 4.4 (Fu’s data).

2.15 Clustering, heatmaps etc

The function plotMDS draws a multi-dimensional scaling plot of the RNA samples in which distances correspond to leading log-fold-changes between each pair of RNA samples. The leading log-fold-change is the average (root-mean-square) of the largest absolute log-fold- changes between each pair of samples. This plot can be viewed as a type of unsupervised clustering. The function also provides the option of computing distances in terms of BCV between each pair of samples instead of leading logFC. Inputing RNA-seq counts to clustering or heatmap routines designed for microarray data is not straight-forward, and the best way to do this is still a matter of research. To draw a heatmap of individual RNA-seq samples, we suggest using moderated log-counts-per-million. This can be calculated by cpm with positive values for prior.count, for example

> logcpm <- cpm(y, prior.count=2, log=TRUE)

25 where y is the normalized DGEList object. This produces a matrix of log2 counts-per-million (logCPM), with undeﬁned values avoided and the poorly deﬁned log-fold-changes for low counts shrunk towards zero. Larger values for prior.count produce more shrinkage. The logCPM values can optionally be converted to RPKM or FPKM by subtracting log2 of gene length, see rpkm().

2.16 Alternative splicing edgeR can also be used to analyze RNA-Seq data at the exon level to detect differential splicing or isoform-specific differential expression. Alternative splicing events are detected by testing for differential exon usage for each gene, that is testing whether the log-fold- changes differ between exons for the same gene. Both exon-level and gene-level tests can be performed simultaneously using the diffSpliceDGE() function in edgeR. The exon-level test tests for the significant difference between the exon’s logFC and the overall logFC for the gene. Two testing methods at the gene-level are provided. The first is to conduct a gene-level statistical test using the exon-level test statistics. Whether it is a likelihood ratio test or a QL F-test depends on the pipeline chosen. The second is to convert the exon-level p-values into a genewise p-value by the Simes’ method. The first method is likely to be powerful for genes in which several exons are differentially spliced. The Simes’ method is likely to be more powerful when only a minority of the exons for a gene are differentially spliced. The top set of most significant spliced genes can be viewed by the topSpliceDGE() function. The exon-level testing results for a gene of interest can be visualized by the plotSpliceDGE() function. For more detailed examples, see the case study in section 4.5 (Pasilla’s data).

2.17 CRISPR-Cas9 and shRNA-seq screen analysis edgeR can also be used to analyze data from CRISPR-Cas9 and shRNA-seq genetic screens as described in Dai et al. (2014) [7]. Screens of this kind typically involve the comparison of two or more cell populations either in the presence or absence of a selective pressure, or as a time-course before and after a selective pressure is applied. The goal is to identify sgRNAs (or shRNAs) whose representation changes (either increases or decreases) suggesting that disrupting the target gene’s function has an eﬀect on the cell. To begin, the processAmplicons function can be used to obtain counts for each sgRNA (or shRNA) in the screen in each sample and organise them in a DGEList for down-stream analysis using either the classic edgeR or GLM pipeline mentioned above. Next, gene set testing methods such as camera and roast can be used to summarize results from multiple sgRNAs or shRNAs targeting the same gene to obtain gene-level results.

26 For a detailed example, see the case study in section 4.6 (CRISPR-Cas9 knockout screen analysis).

27 Chapter 3

Speciﬁc experimental designs

3.1 Introduction

In this chapter, we outline the principles for setting up the design matrix and forming contrasts for some typical experimental designs.

3.2 Two or more groups

3.2.1 Introduction The simplest and most common type of experimental design is that in which a number of experimental conditions are compared on the basis of independent biological replicates of each condition. Suppose that there are three experimental conditions to be compared, treatments A, B and C, say. The samples component of the DGEList data object might look like:

> y$samples group lib.size norm.factors sample.1 A 100001 1 sample.2 A 100002 1 sample.3 B 100003 1 sample.4 B 100004 1 sample.5 C 100005 1

Note that it is not necessary to have multiple replicates for all the conditions, although it is usually desirable to do so. By default, the conditions will be listed in alphabetical order, regardless of the order that the data were read:

> levels(y$samples$group) [1] "A" "B" "C"

28 3.2.2 Classic approach The classic edgeR approach is to make pairwise comparisons between the groups. For example,

> et <- exactTest(y, pair=c("A","B")) > topTags(et) will ﬁnd genes diﬀerentially expressed (DE) in B vs A. Similarly

> et <- exactTest(y, pair=c("A","C")) for C vs A, or

> et <- exactTest(y, pair=c("C","B")) for B vs C. Alternatively, the conditions to be compared can be speciﬁed by number, so that

> et <- exactTest(y, pair=c(3,2)) is equivalent to pair=c("C","B"), given that the second and third levels of group are B and C respectively. Note that the levels of group are in alphabetical order by default, but can be easily changed. Suppose for example that C is a control or reference level to which conditions A and B are to be compared. Then one might redeﬁne the group levels, in a new data object, so that C is the ﬁrst level:

> y2 <- y > y2$samples$group <- relevel(y2$samples$group, ref="C") > levels(y2$samples$group) [1] "C" "A" "B" Now

> et <- exactTest(y2, pair=c("A","B")) would still compare B to A, but

> et <- exactTest(y2, pair=c(1,2)) would now compare A to C. When pair is not speciﬁed, the default is to compare the ﬁrst two group levels, so

> et <- exactTest(y) compares B to A, whereas

> et <- exactTest(y2) compares A to C.

29 3.2.3 GLM approach The glm approach to multiple groups is similar to the classic approach, but permits more general comparisons to be made. The glm approach requires a design matrix to describe the treatment conditions. We will usually use the model.matrix function to construct the design matrix, although it could be constructed manually. There are always many equivalent ways to define this matrix. Perhaps the simplest way is to define a coefficient for the expression level of each group:

> design <- model.matrix(~0+group, data=y$samples) > colnames(design) <- levels(y$samples$group) > design ABC sample.1 1 0 0 sample.2 1 0 0 sample.3 0 1 0 sample.4 0 1 0 sample.5 0 0 1

Here, the 0+ in the model formula is an instruction not to include an intercept column and instead to include a column for each group. One can compare any of the treatment groups using the contrast argument of the glmLRT function. For example,

> fit <- glmFit(y, design) > lrt <- glmLRT(fit, contrast=c(-1,1,0)) > topTags(lrt) will compare B to A. The meaning of the contrast is to make the comparison -1*A + 1*B + 0*C, which is of course is simply B-A. The contrast vector can be constructed using makeContrasts if that is convenient. The above comparison could have been made by

> BvsA <- makeContrasts(B-A, levels=design) > lrt <- glmLRT(fit, contrast=BvsA)

One could make three pairwise comparisons between the groups by

> my.contrasts <- makeContrasts(BvsA=B-A, CvsB=C-B, CvsA=A-C, levels=design) > lrt.BvsA <- glmLRT(fit, contrast=my.contrasts[,"BvsA"]) > topTags(lrt.BvsA) > lrt.CvsB <- glmLRT(fit, contrast=my.contrasts[,"CvsB"]) > topTags(lrt.CvsB) > lrt.CvsA <- glmLRT(fit, contrast=my.contrasts[,"CvsA"]) > topTags(lrt.CvsA) which would compare B to A, C to B and C to A respectively. Any comparison can be made. For example,

30 > lrt <- glmLRT(fit, contrast=c(-0.5,-0.5,1)) would compare C to the average of A and B. Alternatively, this same contrast could have been speciﬁed by

> my.contrast <- makeContrasts(C-(A+B)/2, levels=design) > lrt <- glmLRT(fit, contrast=my.contrast) with the same results.

3.2.4 Questions and contrasts The glm approach allows an infinite variety of contrasts to be tested between the groups. This embarassment of riches leads to the question, which specific contrasts should we test? This answer is that we should form and test those contrasts that correspond to the scientific questions that we want to answer. Each statistical test is an answer to a particular question, and we should make sure that our questions and answers match up. To clarify this a little, we will consider a hypothetical experiment with four groups. The groups correspond to four different types of cells: white and smooth, white and furry, red and smooth and red furry. We will think of white and red as being the major group, and smooth and furry as being a sub-grouping. Suppose the RNA samples look like this: Sample Color Type Group 1 White Smooth A 2 White Smooth A 3 White Furry B 4 White Furry B 5 Red Smooth C 6 Red Smooth C 7 Red Furry D 8 Red Furry D

To decide which contrasts should be made between the four groups, we need to be clear what are our scientific hypotheses. In other words, what are we seeking to show? First, suppose that we wish to find genes that are always higher in red cells than in white cells. Then we will need to form the four contrasts C-A, C-B, D-A and D-B, and select genes that are significantly up for all four contrasts. Or suppose we wish to establish that the difference between Red and White is large compared to the differences between Furry and Smooth. An efficient way to establish this would be to form the three contrasts B-A, D-C and (C+D)/2-(A+B)/2. We could confidently make this assertion for genes for which the third contrast is far more significant than the first two. Even if B-A and D-C are statistically significant, we could still look for genes for which the fold changes for (C+D)/2-(A+B)/2 are much larger than those for B-A or D-C.

31 We might want to find genes that are more highly expressed in Furry cells regardless of color. Then we would test the contrasts B-A and D-C, and look for genes that are significantly up for both contrasts. Or we want to assert that the difference between Furry over Smooth is much the same regardless of color. In that case you need to show that the contrast (B+D)/2-(A+C)/2 (the average Furry effect) is significant for many genes but that (D-C)-(B-A) (the interaction) is not.

3.2.5 A more traditional glm approach A more traditional way to create a design matrix in R is to include an intercept term that represents the ﬁrst level of the factor. We included 0+ in our model formula above. Had we omitted it, the design matrix would have had the same number of columns as above, but the ﬁrst column would be the intercept term and the meanings of the second and third columns would change:

> design <- model.matrix(~group, data=y$samples) > design (Intercept) groupB groupC sample.1 1 0 0 sample.2 1 0 0 sample.3 1 1 0 sample.4 1 1 0 sample.5 1 0 1 Now the first coefficient will measure the baseline logCPM expression level in the first treatment condition (here group A), and the second and third columns are relative to the baseline. Here the second and third coefficients represent B vs A and C vs A respectively. In other words, coef=2 now means B-A and coef=3 means C-A, so

> fit <- glmFit(y, design) > lrt <- glmLRT(fit, coef=2) would test for diﬀerential expression in B vs A. and

> lrt <- glmLRT(fit, coef=3) would test for differential expression in C vs A. This parametrization makes good sense when the first group represents a reference or control group, as all comparison are made with respect to this condition. If we releveled the factor to make level C the first level (see Section 3.2.2), then the design matrix becomes:

> design2 <- model.matrix(~group, data=y2$samples) > design2 (Intercept) groupA groupB sample.1 1 1 0 sample.2 1 1 0

32 sample.3 1 0 1 sample.4 1 0 1 sample.5 1 0 0

Now

> fit2 <- glmFit(y2, design2) > lrt <- glmLRT(fit2, coef=2) compares A to C, and

> lrt <- glmLRT(fit2, coef=3) compares B to C. With this parametrization, one could still compare B to A using

> lrt <- glmLRT(fit2, contrast=c(0,-1,1))

Note that

> lrt <- glmLRT(fit2, coef=1) should not be used. It would test whether the ﬁrst coeﬃcient is zero, but it is not meaningful to compare the logCPM in group A to zero.

3.2.6 An ANOVA-like test for any differences It might be of interest to find genes that are DE between any of the groups, without specifying before-hand which groups might be different. This is analogous to a one-way ANOVA test. In edgeR, this is done by specifying multiple coefficients to glmLRT, when the design matrix includes an intercept term. For example, with fit as defined in the previous section,

> lrt <- glmLRT(fit, coef=2:3) > topTags(lrt) will find any genes that differ between any of the treatment conditions A, B or C. Technically, this procedure tests whether either of the contrasts B-A or C-A are non-zero. Since at least one of these must be non-zero when differences exist, the test will detect any differences. To have this effect, the coef argument should specify all the coefficients except the intercept. Note that this approach does not depend on how the group factor was defined, or how the design matrix was formed, as long as there is an intercept column. For example

> lrt <- glmLRT(fit2, coef=2:3) gives exactly the results, even though fit2 and fit were computed using diﬀerent design matrices. Here fit2 is as deﬁned in the previous section.

33 3.3 Experiments with all combinations of multiple factors

3.3.1 Deﬁning each treatment combination as a group We now consider experiments with more than one experimental factor, but in which every combination of experiment conditions can potentially have a unique eﬀect. For example, suppose that an experiment has been conducted with an active drug and a placebo, at three times from 0 hours to 2 hours, with all samples obtained from independent subjects. The data frame targets describes the treatment conditions applied to each sample:

> targets Treat Time Sample1 Placebo 0h Sample2 Placebo 0h Sample3 Placebo 1h Sample4 Placebo 1h Sample5 Placebo 2h Sample6 Placebo 2h Sample7 Drug 0h Sample8 Drug 0h Sample9 Drug 1h Sample10 Drug 1h Sample11 Drug 2h Sample12 Drug 2h

As always, there are many ways to setup a design matrix. A simple, multi-purpose approach is to combine all the experimental factors into one combined factor:

> Group <- factor(paste(targets$Treat,targets$Time,sep=".")) > cbind(targets,Group=Group) Treat Time Group Sample1 Placebo 0h Placebo.0h Sample2 Placebo 0h Placebo.0h Sample3 Placebo 1h Placebo.1h Sample4 Placebo 1h Placebo.1h Sample5 Placebo 2h Placebo.2h Sample6 Placebo 2h Placebo.2h Sample7 Drug 0h Drug.0h Sample8 Drug 0h Drug.0h Sample9 Drug 1h Drug.1h Sample10 Drug 1h Drug.1h Sample11 Drug 2h Drug.2h Sample12 Drug 2h Drug.2h

Then we can take the same approach as in the previous section on two or more groups. Each treatment time for each treatment drug is a group:

34 > design <- model.matrix(~0+Group) > colnames(design) <- levels(Group) > fit <- glmFit(y, design)

Then we can make any comparisons we wish. For example, we might wish to make the following contrasts:

> my.contrasts <- makeContrasts( + Drug.1vs0 = Drug.1h-Drug.0h, + Drug.2vs0 = Drug.2h-Drug.0h, + Placebo.1vs0 = Placebo.1h-Placebo.0h, + Placebo.2vs0 = Placebo.2h-Placebo.0h, + DrugvsPlacebo.0h = Drug.0h-Placebo.0h, + DrugvsPlacebo.1h = (Drug.1h-Drug.0h)-(Placebo.1h-Placebo.0h), + DrugvsPlacebo.2h = (Drug.2h-Drug.0h)-(Placebo.2h-Placebo.0h), + levels=design)

To ﬁnd genes responding to the drug at 1 hour:

> lrt <- glmLRT(fit, contrast=my.contrasts[,"Drug.1vs0"]) or at 2 hours:

> lrt <- glmLRT(fit, contrast=my.contrasts[,"Drug.2vs0"])

To ﬁnd genes with baseline diﬀerences between the drug and the placebo at 0 hours:

> lrt <- glmLRT(fit, contrast=my.contrasts[,"DrugvsPlacebo.0h"])

To ﬁnd genes that have responded diﬀerently to the drug and the placebo at 2 hours:

> lrt <- glmLRT(fit, contrast=my.contrasts[,"DrugvsPlacebo.2h"])

Of course, it is not compulsory to use makeContrasts to form the contrasts. The coeﬃ- cients are the following:

> colnames(fit) [1] "Drug.0h" "Drug.1h" "Drug.2h" "Placebo.0h" "Placebo.1h" "Placebo.2h" so

> lrt <- glmLRT(fit, contrast=c(-1,0,1,0,0,0)) would ﬁnd the Drug.2vs0 contrast, and

> lrt <- glmLRT(fit, contrast=c(-1,0,1,1,0,-1)) is another way of specifying the DrugvsPlacebo.2h contrast.

35 3.3.2 Nested interaction formulas We generally recommend the approach of the previous section, because it is so explicit and easy to understand. However it may be useful to be aware of more short-hand approach to form the same contrasts in the previous section using a model formula. First, make sure that the placebo is the reference level:

> targets$Treat <- relevel(targets$Treat, ref="Placebo") Then form the design matrix:

> design <- model.matrix(~Treat + Treat:Time, data=targets) > fit <- glmFit(y, design) The meaning of this formula is to consider all the levels of time for each treatment drug separately. The second term is a nested interaction, the interaction of Time within Treat. The coeﬃcient names are:

> colnames(fit) [1] "(Intercept)" "TreatDrug" [3] "TreatPlacebo:Time1h" "TreatDrug:Time1h" [5] "TreatPlacebo:Time2h" "TreatDrug:Time2h" Now most of the above contrasts are directly available as coeﬃcients:

> lrt <- glmLRT(fit, coef=2) is the baseline drug vs placebo comparison,

> lrt <- glmLRT(fit, coef=4) is the drug eﬀect at 1 hour,

> lrt <- glmLRT(fit, coef=6) is the drug eﬀect at 2 hours, and ﬁnally

> lrt <- glmLRT(fit, contrast=c(0,0,0,0-1,1)) is the DrugvsPlacebo.2h contrast.

3.3.3 Treatment eﬀects over all times The nested interaction model makes it easy to ﬁnd genes that respond to the treatment at any time, in a single test. Continuing the above example,

> lrt <- glmLRT(fit, coef=c(4,6)) ﬁnds genes that respond to the treatment at either 1 hour or 2 hours versus the 0 hour baseline. This is analogous to an ANOVA F -test for a normal linear model.

36 3.3.4 Interaction at any time The full interaction formula is

> design <- model.matrix(~Treat * Time, data=targets) which is equivalent to

> design <- model.matrix(~Treat + Time + Treat:Time, data=targets) > fit <- glmFit(y, design)

This formula is primarily useful as a way to conduct an overall test for interaction. The coeﬃcient names are:

> colnames(design) [1] "(Intercept)" "TreatDrug" [3] "Time1h" "Time2h" [5] "TreatDrug:Time1h" "TreatDrug:Time2h"

Now

> lrt <- glmLRT(fit, coef=2) is again the baseline drug vs placebo comparison, but

> lrt <- glmLRT(fit, coef=3) and

> lrt <- glmLRT(fit, coef=4) are the effects of the reference drug, i.e., the effects of the placebo at 1 hour and 2 hours. The last two coefficients give the DrugvsPlacebo.1h and DrugvsPlacebo.2h contrasts, so that

> lrt <- glmLRT(fit, coef=5:6) is useful because it detects genes that respond diﬀerently to the drug, relative to the placebo, at either of the times.

3.4 Additive models and blocking

3.4.1 Paired samples Paired samples occur whenever we compare two treatments and each independent subject in the experiment receives both treatments. Suppose for example that an experiment is conducted to compare a new treatment (T) with a control (C). Suppose that both the control and the treatment are administered to each of three patients. This produces the sample data:

37 FileName Subject Treatment File1 1 C File2 1 T File3 2 C File4 2 T File5 3 C File6 3 T

This is a paired design in which each subject receives both the control and the active treatment. We can therefore compare the treatment to the control for each patient separately, so that baseline diﬀerences between the patients are subtracted out. The design matrix is formed from an additive model formula without an interaction term:

> Subject <- factor(targets$Subject) > Treat <- factor(targets$Treatment, levels=c("C","T")) > design <- model.matrix(~Subject+Treat)

The omission of an interaction term is characteristic of paired designs. We are not interested in the eﬀect of the treatment on an individual patient (which is what an interaction term would examine). Rather we are interested in the average eﬀect of the treatment over a population of patients. As always, the dispersion has to be estimated:

> y <- estimateGLMCommonDisp(y,design) > y <- estimateGLMTrendedDisp(y,design) > y <- estimateGLMTagwiseDisp(y,design)

We proceed to fit a linear model and test for the treatment effect. Note that we can omit the coef argument to glmLRT because the treatment effect is the last coefficient in the model.

> fit <- glmFit(y, design) > lrt <- glmLRT(fit) > topTags(lrt)

This test detects genes that are diﬀerentially expressed in response to the active treatment compared to the control, adjusting for baseline diﬀerences between the patients. This test can be viewed as a generalization of a paired t-test. See the oral carcinomas case study of Section 4.1 for a fully worked analysis with paired samples.

3.4.2 Blocking Paired samples are a simple example of what is called “blocking” in experimental design. The idea of blocking is to compare treatments using experimental subjects that are as similar as possible, so that the treatment diﬀerence stands out as clearly as possible.

38 Suppose for example that we wish to compare three treatments A, B and C using experimental animals. Suppose that animals from the same litter are appreciably more similar than animals from different litters. This might lead to an experimental setup like: FileName Litter Treatment File1 1 A File2 1 B File3 1 C File4 2 B File5 2 A File6 2 C File7 3 C File8 3 B File9 3 A Here it is the differences between the treatments that are of interest. The differences between the litters are not of primary interest, nor are we interested in a treatment effect that occurs for in only one litter, because that would not be reproducible. We can compare the three treatments adjusting for any baseline differences between the litters by fitting an additive model:

> Litter <- factor(targets$Litter) > Treatment <- factor(targets$Treatment) > design <- model.matrix(~Litter+Treatment) This creates a design matrix with five columns: three for the litters and two more for the differences between the treatments. If fit is the fitted model with this design matrix, then we may proceed as follows. To detect genes that are differentially expressed between any of the three treatments, adjusting for litter differences:

> lrt <- glmLRT(fit, coef=4:5) > topTags(lrt) To detect genes that are diﬀerentially expressed in treatment B vs treatment A:

> lrt <- glmLRT(fit, coef=4) > topTags(lrt) To detect genes that are diﬀerentially expressed in treatment C vs treatment A:

> lrt <- glmLRT(fit, coef=5) > topTags(lrt) To detect genes that are diﬀerentially expressed in treatment C vs treatment B:

> lrt <- glmLRT(fit, contrast=c(0,0,0,-1,1)) > topTags(lrt)

39 The advantage of using litter as a blocking variable in the analysis is that this will make the comparison between the treatments more precise, if litter-mates are more alike that animals from different litters. On the other hand, if litter-mates are no more alike than animals from different litters, which might be so for genetically identical inbred laboratory animals, then the above analysis is somewhat inefficient because the litter effects are being estimated unnecessarily. In that case, it would be better to omit litter from the model formula.

3.4.3 Batch effects Another situation in which additive model formulas are used is when correcting for batch effects in an experiment. The situation here is analogous to blocking, the only difference being that the batch effects were probably unintended rather than a deliberate aspect of the experimental design. The analysis is the same as for blocking. The treatments can be adjusted for differences between the batches by using an additive model formula of the form:

> design <- model.matrix(~Batch+Treatment) In this type of analysis, the treatments are compared only within each batch. The analysis is corrected for baseline diﬀerences between the batches. The Arabidopsis case study in Section 4.2 gives a fully worked example with batch eﬀects.

3.5 Comparisons both between and within subjects

Here is a more complex scenario, posed by a poster to the Bioconductor mailing list. The experiment has 18 RNA samples collected from 9 subjects. The samples correspond to cells from 3 healthy patients, either treated or not with a hormone; cells from 3 patients with disease 1, either treated or not with the hormone; and cells from 3 patients with disease 2, either treated or not with the hormone. The targets frame looks like this:

> targets Disease Patient Treatment 1 Healthy 1 None 2 Healthy 1 Hormone 3 Healthy 2 None 4 Healthy 2 Hormone 5 Healthy 3 None 6 Healthy 3 Hormone 7 Disease1 4 None 8 Disease1 4 Hormone 9 Disease1 5 None 10 Disease1 5 Hormone 11 Disease1 6 None 12 Disease1 6 Hormone 13 Disease2 7 None

40 14 Disease2 7 Hormone 15 Disease2 8 None 16 Disease2 8 Hormone 17 Disease2 9 None 18 Disease2 9 Hormone

If all the RNA samples were collected from independent subjects, then this would be nested factorial experiment, from which we would want to estimate the treatment eﬀect for each disease group. As it is, however, we have a paired comparison experiment for each disease group. The feature that makes this experiment complex is that some comparisons (between the diseases) are made between patients while other comparisons (hormone treatment vs no treatment) are made within patients. The design matrix will be easier to construct in R if we re-number the patients within each disease group:

> Patient <- gl(3,2,length=18)

We also deﬁne Disease and Treatment to be factors, with the control state as the ﬁrst level in each case:

> Disease <- factor(targets$Disease, levels=c("Healthy","Disease1","Disease2")) > Treatment <- factor(targets$Treatment, levels=c("None","Hormone"))

This gives us a revised targets frame:

> data.frame(Disease,Patient,Treatment) Disease Patient Treatment 1 Healthy 1 None 2 Healthy 1 Hormone 3 Healthy 2 None 4 Healthy 2 Hormone 5 Healthy 3 None 6 Healthy 3 Hormone 7 Disease1 1 None 8 Disease1 1 Hormone 9 Disease1 2 None 10 Disease1 2 Hormone 11 Disease1 3 None 12 Disease1 3 Hormone 13 Disease2 1 None 14 Disease2 1 Hormone 15 Disease2 2 None 16 Disease2 2 Hormone 17 Disease2 3 None 18 Disease2 3 Hormone

Now we can construct the design matrix. The critical feature to appreciate is that Patient and Treatment are of interest within each disease group, so we use the nested factorial formula

41 discussed in a previous section. The patients are nested with the disease groups, because we have different patients in each group. The treatment is nested within disease groups, because we are interested in the disease-specific treatment effects. The model formula has the main effect for disease plus nested interactions with Patient and Treatment:

> design <- model.matrix(~Disease+Disease:Patient+Disease:Treatment) > colnames(design) [1] "(Intercept)" "DiseaseDisease1" [3] "DiseaseDisease2" "DiseaseHealthy:Patient2" [5] "DiseaseDisease1:Patient2" "DiseaseDisease2:Patient2" [7] "DiseaseHealthy:Patient3" "DiseaseDisease1:Patient3" [9] "DiseaseDisease2:Patient3" "DiseaseHealthy:TreatmentHormone" [11] "DiseaseDisease1:TreatmentHormone" "DiseaseDisease2:TreatmentHormone" After estimating the dispersions (code not shown), we can ﬁt a linear model:

> fit <- glmFit(y, design) To ﬁnd genes responding to the hormone in healthy patients:

> lrt <- glmLRT(fit, coef="DiseaseHealthy:TreatmentHormone") > topTags(lrt) To ﬁnd genes responding to the hormone in disease1 patients:

> lrt <- glmLRT(fit, coef="DiseaseDisease1:TreatmentHormone") > topTags(lrt) To ﬁnd genes responding to the hormone in disease2 patients:

> lrt <- glmLRT(fit, coef="DiseaseDisease2:TreatmentHormone") > topTags(lrt) To ﬁnd genes that respond to the hormone in any disease group:

> lrt <- glmLRT(fit, coef=10:12) > topTags(lrt) To ﬁnd genes that respond diﬀerently to the hormone in disease1 vs healthy patients:

> lrt <- glmLRT(fit, contrast=c(0,0,0,0,0,0,0,0,0,-1,1,0)) > topTags(lrt) To ﬁnd genes that respond diﬀerently to the hormone in disease2 vs healthy patients:

> lrt <- glmLRT(fit, contrast=c(0,0,0,0,0,0,0,0,0,-1,0,1)) > topTags(lrt) To ﬁnd genes that respond diﬀerently to the hormone in disease2 vs disease1 patients:

> lrt <- glmLRT(fit, contrast=c(0,0,0,0,0,0,0,0,0,0,-1,1)) > topTags(lrt)

42 Chapter 4

Case studies

4.1 RNA-Seq of oral carcinomas vs matched normal tissue

4.1.1 Introduction This section provides a detailed analysis of data from a paired design RNA-seq experiment, featuring oral squamous cell carcinomas and matched normal tissue from three patients [32]. The aim of the analysis is to detect genes diﬀerentially expressed between tumor and normal tissue, adjusting for any diﬀerences between the patients. This provides an example of the GLM capabilities of edgeR. RNA was sequenced on an Applied Biosystems SOLiD System 3.0 and reads mapped to the UCSC hg18 reference genome [32]. Read counts, summarised at the level of refSeq transcripts, are available in Table S1 of Tuch et al. [32].

4.1.2 Reading in the data The read counts for the six individual libraries are stored in one tab-delimited ﬁle. To make this ﬁle, we downloaded Table S1 from Tuch et al. [32], deleted some unnecessary columns and edited the column headings slightly:

> rawdata <- read.delim("TableS1.txt", check.names=FALSE, stringsAsFactors=FALSE) > head(rawdata) RefSeqID Symbol NbrOfExons 8N 8T 33N 33T 51N 51T 1 NM_182502 TMPRSS11B 10 2592 3 7805 321 3372 9 2 NM_003280 TNNC1 6 1684 0 1787 7 4894 559 3 NM_152381 XIRP2 10 9915 15 10396 48 23309 7181 4 NM_022438 MAL 3 2496 2 3585 239 1596 7 5 NM_001100112 MYH2 40 4389 7 7944 16 9262 1818 6 NM_017534 MYH2 40 4402 7 7943 16 9244 1815

43 For easy manipulation, we put the data into a DGEList object:

> library(edgeR) > y <- DGEList(counts=rawdata[,4:9], genes=rawdata[,1:3])

4.1.3 Annotation The study by Tuch et al. [32] was undertaken a few years ago, so not all of the RefSeq IDs provided by match RefSeq IDs currently in use. We retain only those transcripts with IDs in the current NCBI annotation, which is provided by the org.HS.eg.db package:

> library(org.Hs.eg.db) > idfound <- y$genes$RefSeqID %in% mappedRkeys(org.Hs.egREFSEQ) > y <- y[idfound,] > dim(y) [1] 15559 6

We add Entrez Gene IDs to the annotation:

> egREFSEQ <- toTable(org.Hs.egREFSEQ) > head(egREFSEQ) gene_id accession 1 1 NM_130786 2 1 NP_570602 3 2 NM_000014 4 2 NP_000005 5 2 XM_006719056 6 2 XP_006719119 > m <- match(y$genes$RefSeqID, egREFSEQ$accession) > y$genes$EntrezGene <- egREFSEQ$gene_id[m]

Now use the Entrez Gene IDs to update the gene symbols:

> egSYMBOL <- toTable(org.Hs.egSYMBOL) > head(egSYMBOL) gene_id symbol 1 1 A1BG 2 2 A2M 3 3 A2MP1 4 9 NAT1 5 10 NAT2 6 11 NATP > m <- match(y$genes$EntrezGene, egSYMBOL$gene_id) > y$genes$Symbol <- egSYMBOL$symbol[m] > head(y$genes)

44 RefSeqID Symbol NbrOfExons EntrezGene 1 NM_182502 TMPRSS11B 10 132724 2 NM_003280 TNNC1 6 7134 3 NM_152381 XIRP2 10 129446 4 NM_022438 MAL 3 4118 5 NM_001100112 MYH2 40 4620 6 NM_017534 MYH2 40 4620

4.1.4 Filtering and normalization Diﬀerent RefSeq transcripts for the same gene symbol count predominantly the same reads. So we keep one transcript for each gene symbol. We choose the transcript with highest overall count:

> o <- order(rowSums(y$counts), decreasing=TRUE) > y <- y[o,] > d <- duplicated(y$genes$Symbol) > y <- y[!d,] > nrow(y) [1] 10523

Normally we would also ﬁlter lowly expressed genes. For this data, all transcripts already have at least 50 reads for all samples of at least one of the tissues types. Recompute the library sizes:

> y$samples$lib.size <- colSums(y$counts)

Use Entrez Gene IDs as row names:

> rownames(y$counts) <- rownames(y$genes) <- y$genes$EntrezGene > y$genes$EntrezGene <- NULL

TMM normalization is applied to this dataset to account for compositional diﬀerence between the libraries.

> y <- calcNormFactors(y) > y$samples group lib.size norm.factors 8N 1 7992800 1.146 8T 1 7374090 1.086 33N 1 15759922 0.673 33T 1 14050463 0.974 51N 1 21547308 1.032 51T 1 15199698 1.190

45 4.1.5 Data exploration The ﬁrst step of an analysis should be to examine the samples for outliers and for other relationships. The function plotMDS produces a plot in which distances between samples correspond to leading biological coeﬃcient of variation (BCV) between those samples:

> plotMDS(y)

2.0 51T 1.5

1.0 51N 0.5

8T 0.0

Leading logFC dim 2 8N

−1.0 33T 33N

−3 −2 −1 0 1 2

Leading logFC dim 1

In the plot, dimension 1 separates the tumor from the normal samples, while dimension 2 roughly corresponds to patient number. This conﬁrms the paired nature of the samples. The tumor samples appear more heterogeneous than the normal samples.

4.1.6 The design matrix Before we fit negative binomial GLMs, we need to define our design matrix based on the experimental design. Here we want to test for differential expression between tumour and normal tissues within patients, i.e. adjusting for differences between patients. In statistical terms, this is an additive linear model with patient as the blocking factor:

> Patient <- factor(c(8,8,33,33,51,51)) > Tissue <- factor(c("N","T","N","T","N","T")) > data.frame(Sample=colnames(y),Patient,Tissue) Sample Patient Tissue 1 8N 8 N 2 8T 8 T 3 33N 33 N

46 4 33T 33 T 5 51N 51 N 6 51T 51 T > design <- model.matrix(~Patient+Tissue) > rownames(design) <- colnames(y) > design (Intercept) Patient33 Patient51 TissueT 8N 1 0 0 0 8T 1 0 0 1 33N 1 1 0 0 33T 1 1 0 1 51N 1 0 1 0 51T 1 0 1 1 attr(,"assign") [1] 0 1 1 2 attr(,"contrasts") attr(,"contrasts")$Patient [1] "contr.treatment" attr(,"contrasts")$Tissue [1] "contr.treatment"

This sort of additive model is appropriate for paired designs, or experiments with batch eﬀects.

4.1.7 Estimating the dispersion We estimate the NB dispersion for the dataset.

> y <- estimateDisp(y, design, robust=TRUE) > y$common.dispersion [1] 0.159

The square root of the common dispersion gives the coeﬃcient of variation of biological variation. Here the common dispersion is found to be 0.159, so the coeﬃcient of biological variation is around 0.4. The dispersion estimates can be viewed in a BCV plot:

> plotBCV(y)

47 4.1.8 Diﬀerential expression Now proceed to determine diﬀerentially expressed genes. Fit genewise glms:

> fit <- glmFit(y, design)

Conduct likelihood ratio tests for tumour vs normal tissue diﬀerences and show the top genes:

> lrt <- glmLRT(fit) > topTags(lrt) Coefficient: TissueT RefSeqID Symbol NbrOfExons logFC logCPM LR PValue FDR 5737 NM_001039585 PTGFR 4 -5.18 4.74 98.7 2.98e-23 3.14e-19 5744 NM_002820 PTHLH 4 3.97 6.21 92.1 8.10e-22 4.26e-18 3479 NM_001111283 IGF1 5 -3.99 5.71 86.5 1.38e-20 4.83e-17 1288 NM_033641 COL4A6 45 3.66 5.71 77.5 1.32e-18 3.47e-15 10351 NM_007168 ABCA8 38 -3.98 4.94 75.9 2.97e-18 6.24e-15 5837 NM_005609 PYGM 20 -5.48 5.99 75.4 3.82e-18 6.70e-15 487 NM_004320 ATP2A1 23 -4.62 5.96 74.8 5.16e-18 7.75e-15 27179 NM_014440 IL36A 4 -6.17 5.40 72.2 1.96e-17 2.58e-14 196374 NM_173352 KRT78 9 -4.25 7.61 70.8 3.98e-17 4.66e-14 83699 NM_031469 SH3BGRL2 4 -3.93 5.53 67.8 1.83e-16 1.93e-13

Note that glmLRT has conducted a test for the last coeﬃcient in the linear model, which we can see is the tumor vs normal tissue eﬀect:

> colnames(design)

48 [1] "(Intercept)" "Patient33" "Patient51" "TissueT"

The genewise tests are for tumor vs normal diﬀerential expression, adjusting for baseline diﬀerences between the three patients. The tests can be viewed as analogous to paired t-tests. The top DE tags have tiny p-values and FDR values, as well as large fold changes. Here’s a closer look at the counts-per-million in individual samples for the top genes:

> o <- order(lrt$table$PValue) > cpm(y)[o[1:10],] 8N 8T 33N 33T 51N 51T 5737 49.69 0.874 27.08 0.877 78.10 2.5425 5744 7.32 95.799 11.79 204.034 6.88 116.2917 3479 50.24 3.123 32.36 1.901 211.59 14.2048 1288 12.12 140.138 6.32 94.378 4.86 56.8193 10351 52.64 3.123 39.43 2.120 79.18 6.0799 5837 152.80 2.748 119.53 1.170 97.67 5.6930 487 107.91 3.123 146.98 3.801 102.80 8.8987 27179 40.08 1.249 172.08 3.290 36.08 0.0553 196374 372.22 20.733 580.96 47.737 145.05 4.5323 83699 96.22 5.121 117.08 5.410 48.18 5.4166

We see that all the top genes have consistent tumour vs normal changes for the three patients. The total number of diﬀerentially expressed genes at 5% FDR is given by:

> summary(de <- decideTestsDGE(lrt)) [,1] -1 938 0 9255 1 330

Plot log-fold change against log-counts per million, with DE genes highlighted:

> detags <- rownames(y)[as.logical(de)] > plotSmear(lrt, de.tags=detags) > abline(h=c(-1, 1), col="blue")

49 The blue lines indicate 2-fold changes.

4.1.9 Gene ontology analysis We perform a gene ontology analysis focusing on the ontology of biological process (BP). The genes up-regulated in the tumors tend to be associated with cell diﬀerentiation, cell migration and tissue morphogenesis:

> go <- goana(lrt) > topGO(go, ont="BP", sort="Up", n=30) Term Ont N Up Down P.Up P.Down GO:0040011 locomotion BP 1142 87 163 3.13e-15 2.39e-10 GO:0006928 movement of cell or subcellular component BP 1235 85 182 2.38e-12 8.40e-13 GO:0016477 cell migration BP 791 61 128 7.08e-11 7.34e-12 GO:0048870 cell motility BP 832 62 130 1.99e-10 5.96e-11 GO:0051674 localization of cell BP 832 62 130 1.99e-10 5.96e-11 GO:0030154 cell differentiation BP 2249 121 285 3.12e-10 9.69e-12 GO:0009888 tissue development BP 1130 74 179 9.87e-10 1.33e-15 GO:0030198 extracellular matrix organization BP 278 31 52 1.23e-09 2.04e-07 GO:0043062 extracellular structure organization BP 278 31 52 1.23e-09 2.04e-07 GO:0007155 cell adhesion BP 876 62 149 1.60e-09 1.26e-15 GO:0044707 single-multicellular organism process BP 3532 165 439 1.65e-09 9.00e-19 GO:0022610 biological adhesion BP 880 62 150 1.91e-09 8.15e-16 GO:0048699 generation of neurons BP 987 66 116 4.39e-09 1.06e-03 GO:0060429 epithelium development BP 712 53 96 5.48e-09 2.22e-05 GO:0022008 neurogenesis BP 1042 68 122 6.61e-09 9.04e-04 GO:0007275 multicellular organism development BP 2921 141 353 9.92e-09 4.67e-12 GO:0048869 cellular developmental process BP 2418 122 296 1.59e-08 2.06e-10

50 GO:0048731 system development BP 2624 129 334 2.35e-08 1.77e-14 GO:0032501 multicellular organismal process BP 3756 168 487 3.54e-08 7.79e-27 GO:0048729 tissue morphogenesis BP 411 36 56 3.73e-08 9.23e-04 GO:0022617 extracellular matrix disassembly BP 94 16 12 4.23e-08 1.34e-01 GO:0009887 organ morphogenesis BP 570 44 81 4.54e-08 1.54e-05 GO:0006775 fat-soluble vitamin metabolic process BP 33 10 1 4.91e-08 9.55e-01 GO:0048513 animal organ development BP 1891 100 259 6.53e-08 1.70e-14 GO:0009653 anatomical structure morphogenesis BP 1745 94 238 8.11e-08 5.39e-13 GO:0048856 anatomical structure development BP 3091 143 384 1.34e-07 1.76e-15 GO:0030182 neuron differentiation BP 915 58 109 2.98e-07 9.44e-04 GO:0002009 morphogenesis of an epithelium BP 339 30 39 4.42e-07 6.18e-02 GO:0009605 response to external stimulus BP 1483 81 186 5.21e-07 3.27e-07 GO:0032502 developmental process BP 3453 153 405 6.15e-07 2.91e-12

4.1.10 Setup This analysis was conducted on:

> sessionInfo() R version 3.3.0 beta (2016-04-14 r70486) Platform: x86_64-w64-mingw32/x64 (64-bit) Running under: Windows 7 x64 (build 7601) Service Pack 1 locale: [1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252 [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C [5] LC_TIME=English_Australia.1252 attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets methods base other attached packages: [1] org.Hs.eg.db_3.3.0 RSQLite_1.0.0 DBI_0.3.1 AnnotationDbi_1.33.11 [5] IRanges_2.5.46 S4Vectors_0.9.51 Biobase_2.31.3 BiocGenerics_0.17.5 [9] edgeR_3.13.9 limma_3.27.19 loaded via a namespace (and not attached): [1] locfit_1.5-9.1 lattice_0.20-33 GO.db_3.3.0 grid_3.3.0 splines_3.3.0 statmod_1.4.24 [7] tools_3.3.0

51 4.2 RNA-Seq of pathogen inoculated arabidopsis with batch eﬀects

4.2.1 Introduction This case study re-analyses Arabidopsis thaliana RNA-Seq data described by Cumbie et al. [6]. Summarized count data is available as a data object in the CRAN package NBPSeq comparing ∆hrcC challenged and mock-inoculated samples [6]. Samples were collected in three batches, and adjustment for batch effects proves to be important. The aim of the analysis therefore is to detect genes differentially expressed in response to ∆hrcC challenge, while correcting for any differences between the batches.

4.2.2 RNA samples Pseudomonas syringae is a bacterium often used to study plant reactions to pathogens. In this experiment, six-week old Arabidopsis plants were inoculated with the ∆hrcC mutant of P. syringae, after which total RNA was extracted from leaves. Control plants were inoculated with a mock pathogen. Three biological replicates of the experiment were conducted at separate times and using independently grown plants and bacteria. The six RNA samples were sequenced one per lane on an Illumina Genome Analyzer. Reads were aligned and summarized per gene using GENE-counter. The reference genome was derived from the TAIR9 genome release (www.arabidopsis.org).

4.2.3 Loading the data Load the data from the NBPSeq package:

> library(NBPSeq) > library(edgeR) > data(arab) > head(arab) mock1 mock2 mock3 hrcc1 hrcc2 hrcc3 AT1G01010 35 77 40 46 64 60 AT1G01020 43 45 32 43 39 49 AT1G01030 16 24 26 27 35 20 AT1G01040 72 43 64 66 25 90 AT1G01050 49 78 90 67 45 60 AT1G01060 0 15 2 0 21 8

There are two experimental factors, treatment (hrcc vs mock) and the time that each replicate was conducted:

52 > Treat <- factor(substring(colnames(arab),1,4)) > Treat <- relevel(Treat, ref="mock") > Time <- factor(substring(colnames(arab),5,5))

We then create a DGEList object:

> y <- DGEList(counts=arab, group=Treat)

4.2.4 Filtering and normalization There is no purpose in analysing genes that are not expressed in either experimental condition. We consider a gene to be expressed at a reasonable level in a sample if it has at least two counts for each million mapped reads in that sample. This cutoﬀ is ad hoc, but serves to require at least 4–6 reads in this case. Since this experiment has three replicates for each condition, a gene should be expressed in at least three samples if it responds to at least one condition. Hence we keep genes with at least two counts per million (CPM) in at least three samples:

> keep <- rowSums(cpm(y)>2) >= 3 > table(keep) keep FALSE TRUE 9696 16526 > y <- y[keep, , keep.lib.sizes=FALSE]

Note that the filtering does not use knowledge of what treatment corresponds to each sample, so the filtering does not bias the subsequent differential expression analysis. The TMM normalization is applied to account for the compositional biases:

> y <- calcNormFactors(y) > y$samples group lib.size norm.factors mock1 mock 1896802 0.979 mock2 mock 1898690 1.054 mock3 mock 3249396 0.903 hrcc1 hrcc 2119367 1.051 hrcc2 hrcc 1264927 1.096 hrcc3 hrcc 3516253 0.932

4.2.5 Data exploration An MDS plot shows the relative similarities of the six samples.

> plotMDS(y)

53 mock2 1.5 1.0 mock1 mock3 0.5 0.0 Leading logFC dim 2 −0.5 hrcc2 hrcc1 −1.0 hrcc3

−2 −1 0 1

Leading logFC dim 1

Distances on an MDS plot of a DGEList object correspond to leading log-fold-change between each pair of samples. Leading log-fold-change is the root-mean-square average of the largest log2-fold-changes between each pair of samples. Each pair of samples extracted at each time tend to cluster together, suggesting a batch eﬀect. The hrcc treated samples tend to be below the mock samples for each time, suggesting a treatment eﬀect within each time. The two samples at time 1 are less consistent than at times 2 and 3. To examine further consistency of the three replicates, we compute predictive log2-fold- changes (logFC) for the treatment separately for the three times. > design <- model.matrix(~Time+Time:Treat) > logFC <- predFC(y,design,prior.count=1,dispersion=0.05) The logFC at the three times are positively correlated with one another, as we would hope: > cor(logFC[,4:6]) Time1:Treathrcc Time2:Treathrcc Time3:Treathrcc Time1:Treathrcc 1.000 0.315 0.400 Time2:Treathrcc 0.315 1.000 0.437 Time3:Treathrcc 0.400 0.437 1.000 The correlation is highest between times 2 and 3.

4.2.6 The design matrix Before we fit GLMs, we need to define our design matrix based on the experimental design. We want to test for differential expressions between ∆hrcC challenged and mock-inoculated samples within batches, i.e. adjusting for differences between batches. In statistical terms, this is an additive linear model. So the design matrix is created as:

54 > design <- model.matrix(~Time+Treat) > rownames(design) <- colnames(y) > design (Intercept) Time2 Time3 Treathrcc mock1 1 0 0 0 mock2 1 1 0 0 mock3 1 0 1 0 hrcc1 1 0 0 1 hrcc2 1 1 0 1 hrcc3 1 0 1 1 attr(,"assign") [1] 0 1 1 2 attr(,"contrasts") attr(,"contrasts")$Time [1] "contr.treatment" attr(,"contrasts")$Treat [1] "contr.treatment"

4.2.7 Estimating the dispersion Estimate the genewise dispersion estimates over all genes, allowing for a possible abundance trend. The estimation is also robustiﬁed against potential outlier genes.

> y <- estimateDisp(y, design, robust=TRUE) > y$common.dispersion [1] 0.0705 > plotBCV(y)

55 The square root of dispersion is the coeﬃcient of biological variation (BCV). The common BCV is on the high side, considering that this is a designed experiment using genetically identical plants. The trended dispersion shows a decreasing trend with expression level. At low logCPM, the dispersions are very large indeed. Note that only the trended dispersion is used under the quasi-likelihood (QL) pipeline. The tagwise and common estimates are shown here but will not be used further. The QL dispersions can be estimated using the glmQLFit function, and then be visualized with the plotQLDisp function.

> fit <- glmQLFit(y, design, robust=TRUE) > plotQLDisp(fit)

4.2.8 Differential expression Now we test for significant differential expression in each gene using the QL F-test. First we check whether there was a genuine need to adjust for the experimental times. We do this by testing for differential expression between the three times. There is considerable differential expression, justifying our decision to adjust for the batch effect:

> qlf <- glmQLFTest(fit, coef=2:3) > topTags(qlf) Coefficient: Time2 Time3 logFC.Time2 logFC.Time3 logCPM F PValue FDR AT5G66800 5.58 -1.065 5.48 150.1 8.93e-10 1.48e-05 AT5G23000 5.58 -0.292 5.71 127.5 2.48e-09 2.05e-05

56 AT5G31702 5.83 -2.568 5.95 113.9 5.03e-09 2.77e-05 AT2G45830 5.42 -0.589 4.71 108.4 6.84e-09 2.83e-05 AT3G33004 4.81 -1.763 5.63 102.8 9.47e-09 3.13e-05 AT2G11230 3.50 -1.532 5.60 98.7 1.22e-08 3.36e-05 AT2G07782 3.48 -1.616 5.28 93.5 1.70e-08 4.01e-05 AT2G18193 3.05 -2.396 5.08 84.8 3.09e-08 6.04e-05 AT2G23910 3.59 -0.384 5.13 83.9 3.29e-08 6.04e-05 AT5G54830 3.07 -0.367 6.07 79.7 4.51e-08 7.31e-05 > FDR <- p.adjust(qlf$table$PValue, method="BH") > sum(FDR < 0.05) [1] 1628

Now conduct QL F-tests for the pathogen effect and show the top genes. By default, the test is for the last coefficient in the design matrix, which in this case is the treatment effect:

> qlf <- glmQLFTest(fit) > topTags(qlf) Coefficient: Treathrcc logFC logCPM F PValue FDR AT2G19190 4.50 7.37 304 1.83e-10 2.62e-06 AT2G39530 4.34 6.71 278 3.17e-10 2.62e-06 AT3G46280 4.78 8.10 247 6.70e-10 2.78e-06 AT2G39380 4.94 5.77 247 6.72e-10 2.78e-06 AT1G51800 3.97 7.71 232 9.92e-10 3.28e-06 AT1G51850 5.32 5.42 209 1.89e-09 4.30e-06 AT5G48430 6.32 6.73 203 2.30e-09 4.30e-06 AT2G44370 5.41 5.20 200 2.50e-09 4.30e-06 AT1G51820 4.34 6.37 198 2.64e-09 4.30e-06 AT3G55150 5.78 4.90 196 2.80e-09 4.30e-06

Here’s a closer look at the individual counts-per-million for the top genes. The top genes are very consistent across the three replicates:

> top <- rownames(topTags(qlf)) > cpm(y)[top,] mock1 mock2 mock3 hrcc1 hrcc2 hrcc3 AT2G19190 16.696 12.0 13.29 341.3 254.7 351.1 AT2G39530 7.001 9.0 13.29 158.1 191.9 243.1 AT3G46280 18.850 17.0 18.40 384.8 374.5 820.9 AT2G39380 2.154 3.0 4.77 91.6 84.4 135.1 AT1G51800 29.083 16.5 30.66 362.4 347.8 464.0 AT1G51850 1.077 1.0 3.75 78.1 56.3 108.9 AT5G48430 4.309 4.5 0.00 189.1 314.6 125.1 AT2G44370 2.154 1.0 1.70 57.0 67.1 86.0 AT1G51820 9.694 7.5 6.13 121.2 156.6 191.3 AT3G55150 0.539 1.0 1.36 43.1 64.9 64.4

57 The total number of genes signiﬁcantly up-regulated or down-regulated at 5% FDR is summarized as follows:

> summary(dt <- decideTestsDGE(qlf)) [,1] -1 837 0 14797 1 892

We can pick out which genes are DE:

> isDE <- as.logical(dt) > DEnames <- rownames(y)[isDE]

Then we can plot all the logFCs against average count size, highlighting the DE genes:

> plotSmear(qlf, de.tags=DEnames) > abline(h=c(-1,1), col="blue")

The blue lines indicate 2-fold up or down.

4.2.9 Setup This analysis was conducted on:

> sessionInfo()

58 R version 3.3.0 beta (2016-04-14 r70486) Platform: x86_64-w64-mingw32/x64 (64-bit) Running under: Windows 7 x64 (build 7601) Service Pack 1 locale: [1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252 [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C [5] LC_TIME=English_Australia.1252 attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets methods base other attached packages: [1] NBPSeq_0.3.0 org.Hs.eg.db_3.3.0 RSQLite_1.0.0 DBI_0.3.1 [5] AnnotationDbi_1.33.11 IRanges_2.5.46 S4Vectors_0.9.51 Biobase_2.31.3 [9] BiocGenerics_0.17.5 edgeR_3.13.9 limma_3.27.19 loaded via a namespace (and not attached): [1] Rcpp_0.12.4.5 magrittr_1.5 splines_3.3.0 munsell_0.4.3 statmod_1.4.24 [6] colorspace_1.2-6 lattice_0.20-33 stringr_1.0.0 plyr_1.8.3 tools_3.3.0 [11] grid_3.3.0 gtable_0.2.0 reshape2_1.4.1 ggplot2_2.1.0 qvalue_2.3.2 [16] stringi_1.0-1 GO.db_3.3.0 scales_0.4.0 locfit_1.5-9.1

4.3 Proﬁles of Yoruba HapMap individuals

4.3.1 Background RNA-Seq profiles were made of cell lines derived from lymphoblastoid cells from 69 different Yoruba individuals from Ibadan, Nigeria [22] [23]. The profiles were generated as part of the International HapMap project [10]. RNA from each individual was sequenced on at least two lanes of an Illumina Genome Analyser 2, and mapped reads to the human genome using MAQ v0.6.8. The study group here is essentially an opportunity sample and the individuals are likely to be genetically diverse. In this analysis we look at genes that are differentially expressed between males and female.

4.3.2 Loading the data Read counts summarized by Ensembl gene identiﬁers are available in the tweeDEseqCount- Data package:

> library(tweeDEseqCountData) > data(pickrell1) > Counts <- exprs(pickrell1.eset) > dim(Counts)

59 [1] 38415 69

> Counts[1:5,1:5]

NA18486 NA18498 NA18499 NA18501 NA18502 ENSG00000127720 6 32 14 35 14 ENSG00000242018 20 21 24 22 16 ENSG00000224440 0 0 0 0 0 ENSG00000214453 0 0 0 0 0 ENSG00000237787 0 0 1 0 0

In this analysis we will compare female with male individuals.

> Gender <- pickrell1.eset$gender > table(Gender)

Gender female male 40 29

> rm(pickrell1.eset)

Annotation for each Ensemble gene is also available from the tweeDEseqCountData package:

> data(annotEnsembl63) > annot <- annotEnsembl63[,c("Symbol","Chr")] > annot[1:5,]

Symbol Chr ENSG00000252775 U7 5 ENSG00000207459 U6 5 ENSG00000252899 U7 5 ENSG00000201298 U6 5 ENSG00000222266 U6 5

> rm(annotEnsembl63)

Form a DGEList object combining the counts and associated annotation:

> library(edgeR) > y <- DGEList(counts=Counts, genes=annot[rownames(Counts),])

60 4.3.3 Filtering and normalization Keep genes with least 1 count-per-million reads (cpm) in at least 20 samples:

> isexpr <- rowSums(cpm(y)>1) >= 20

Keep only genes with deﬁned annotation, and recompute library sizes:

> hasannot <- rowSums(is.na(y$genes))==0 > y <- y[isexpr & hasannot, , keep.lib.sizes=FALSE] > dim(y)

[1] 17310 69

The library sizes vary from about 5 million to over 15 million:

> barplot(y$samples$lib.size*1e-6, names=1:69, ylab="Library size (millions)")

Apply TMM normalization to account for the composition biases:

> y <- calcNormFactors(y) > head(y$samples)

group lib.size norm.factors NA18486 1 7749527 0.939 NA18498 1 13612983 1.110 NA18499 1 8569631 0.963 NA18501 1 8595024 1.201 NA18502 1 13375275 0.938 NA18504 1 9881732 0.979

61 4.3.4 Estimating the dispersion We are interested in the diﬀerences between male and female. Hence, we create a design matrix using the gender factor. We estimate the NB dispersion using estimateDisp. The estimation is robustiﬁed against potential outlier genes.

> design <- model.matrix(~Gender) > y <- estimateDisp(y, design, robust=TRUE) > plotBCV(y)

We then estimate the QL dispersions around the dispersion trend using glmQLFit. The large number of cases and the high variability means that the QL dispersions are not squeezed very heavily from the raw values:

> fit <- glmQLFit(y, design, robust=TRUE) > plotQLDisp(fit)

62 4.3.5 Differential expression Now find genes differentially expressed between male and females. Positive log-fold-changes mean higher expression in males. The highly ranked genes are mostly on the X or Y chro- mosomes. Top ranked is the famous XIST gene, which is known to be expressed only in females.

> qlf <- glmQLFTest(fit) > topTags(qlf,n=15)

Coefficient: Gendermale Symbol Chr logFC logCPM F PValue FDR ENSG00000229807 XIST X -9.49 7.249 1213 1.03e-46 1.78e-42 ENSG00000099749 CYorf15A Y 4.28 1.757 857 1.19e-41 1.03e-37 ENSG00000131002 CYorf15B Y 5.63 2.055 587 2.66e-36 1.31e-32 ENSG00000157828 RPS4Y2 Y 3.18 4.207 585 3.02e-36 1.31e-32 ENSG00000233864 TTTY15 Y 4.84 1.254 538 4.42e-35 1.53e-31 ENSG00000198692 EIF1AY Y 2.36 3.247 376 3.04e-30 8.78e-27 ENSG00000165246 NLGN4Y Y 5.09 1.676 303 1.70e-27 4.21e-24 ENSG00000183878 UTY Y 1.86 3.137 253 3.24e-25 7.01e-22 ENSG00000243209 AC010889.1 Y 2.66 0.797 232 3.63e-24 6.29e-21 ENSG00000129824 RPS4Y1 Y 2.53 5.401 232 3.63e-24 6.29e-21 ENSG00000012817 KDM5D Y 1.47 4.950 222 1.16e-23 1.82e-20 ENSG00000213318 RP11-331F4.1 16 3.67 3.688 217 2.87e-23 4.13e-20 ENSG00000067048 DDX3Y Y 1.62 5.621 181 2.48e-21 3.30e-18 ENSG00000146938 NLGN4X X 3.94 1.048 139 1.81e-18 2.24e-15 ENSG00000232928 RP13-204A15.4 X 1.44 3.558 111 3.19e-16 3.68e-13

63 > summary(decideTestsDGE(qlf))

[,1] -1 46 0 17243 1 21

4.3.6 Gene set testing The tweeDEseqCountData package includes a list of genes belonging to the male-speciﬁc region of chromosome Y, and a list of genes located in the X chromosome that have been reported to escape X-inactivation. We expect genes in the ﬁrst list to be up-regulated in males, whereas genes in the second list should be up-regulated in females.

> data(genderGenes) > Ymale <- rownames(y) %in% msYgenes > Xescape <- rownames(y) %in% XiEgenes

Roast gene set tests by fry() confirm that the male-specific genes are significantly up as a group in our comparison of males with females, whereas the X genes are significantly down as a group [33].

> index <- list(Y=Ymale, X=Xescape) > fry(y, index=index, design=design)

NGenes Direction PValue FDR PValue.Mixed FDR.Mixed Y 12 Up 7.04e-46 1.41e-45 5.86e-11 5.86e-11 X 46 Down 7.25e-17 7.25e-17 2.28e-66 4.55e-66

A barcode plot can be produced to visualize the results. Genes are ranked from left to right by decreasing log-fold-change in the background of the barcode plot. Genes in the set of msYgenes are represented by red bars whereas genes in the set of XiEgenes are represented by blue bars. The line above the barcode shows the relative local enrichment of the vertical bars in each part of the plot. This particular plot suggests that the male-speciﬁc genes tend to have large positive log-fold-changes, whereas the X genes tend to have large negative log-fold-changes.

> barcodeplot(qlf$table$logFC, index[[1]], index[[2]])

64 The results from competitive camera gene sets tests are even more convincing [34]. The positive intergene correlations here show that the genes in each set tend to be biologically correlated:

> camera(y, index, design)

NGenes Correlation Direction PValue FDR Y 12 0.0846 Up 4.18e-39 8.36e-39 X 46 0.0239 Down 1.34e-12 1.34e-12

See where the X and Y genes fall on the MA plot:

> with(qlf$table, plot(logCPM,logFC,pch=16,cex=0.2)) > with(qlf$table, points(logCPM[Xescape],logFC[Xescape],pch=16,col="blue")) > with(qlf$table, points(logCPM[Ymale],logFC[Ymale],pch=16,col="red")) > legend("bottomleft",legend=c("Ymale genes","Xescape genes"),pch=16,,col=c("red","blue"))

65 4.3.7 Setup This analysis was conducted on:

> sessionInfo()

R version 3.3.0 beta (2016-04-14 r70486) Platform: x86_64-w64-mingw32/x64 (64-bit) Running under: Windows 7 x64 (build 7601) Service Pack 1 locale: [1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252 [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C [5] LC_TIME=English_Australia.1252 attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets methods base other attached packages: [1] tweeDEseqCountData_1.9.0 NBPSeq_0.3.0 org.Hs.eg.db_3.3.0 [4] RSQLite_1.0.0 DBI_0.3.1 AnnotationDbi_1.33.11 [7] IRanges_2.5.46 S4Vectors_0.9.51 Biobase_2.31.3 [10] BiocGenerics_0.17.5 edgeR_3.13.9 limma_3.27.19 loaded via a namespace (and not attached): [1] Rcpp_0.12.4.5 magrittr_1.5 splines_3.3.0 munsell_0.4.3 statmod_1.4.24 [6] colorspace_1.2-6 lattice_0.20-33 stringr_1.0.0 plyr_1.8.3 tools_3.3.0

66 [11] grid_3.3.0 gtable_0.2.0 reshape2_1.4.1 ggplot2_2.1.0 qvalue_2.3.2 [16] stringi_1.0-1 GO.db_3.3.0 scales_0.4.0 locfit_1.5-9.1

4.4 RNA-Seq proﬁles of mouse mammary gland

4.4.1 Introduction The RNA-Seq data of this case study is described in Fu et al. [8]. The sequence and count data are publicly available from the Gene Expression Omnibus (GEO) at the series accession number GSE60450. This study examines the expression proﬁles of basal stem-cell enriched cells (B) and committed luminal cells (L) in the mammary gland of virgin, pregnant and lactating mice. Six groups are present, with one for each combination of cell type and mouse status. Each group contains two biological replicates. This is summarized in the table below, where the basal and luminal cell types are abbreviated with B and L respectively.

> targets <- read.delim("targets.txt", header=TRUE) > targets

FileName GEOAccession CellType Status 1 SRR1552450.fastq GSM1480297 B virgin 2 SRR1552451.fastq GSM1480298 B virgin 3 SRR1552452.fastq GSM1480299 B pregnant 4 SRR1552453.fastq GSM1480300 B pregnant 5 SRR1552454.fastq GSM1480301 B lactate 6 SRR1552455.fastq GSM1480302 B lactate 7 SRR1552444.fastq GSM1480291 L virgin 8 SRR1552445.fastq GSM1480292 L virgin 9 SRR1552446.fastq GSM1480293 L pregnant 10 SRR1552447.fastq GSM1480294 L pregnant 11 SRR1552448.fastq GSM1480295 L lactate 12 SRR1552449.fastq GSM1480296 L lactate

The name of the file containing the read sequences for each library is also shown. Each file is downloaded from the Sequence Read Archive and has an accession number starting with SRR, e.g., SRR1552450 for the first library in targets.

4.4.2 Read alignment and processing Prior to read alignment, these ﬁles are converted into the FASTQ format using the fastq-dump utility from the SRA Toolkit. See http://www.ncbi.nlm.nih.gov/books/NBK158900 for how to download and use the SRA Toolkit.

67 Before the differential expression analysis can proceed, these reads must be aligned to the mouse genome and counted into annotated genes. This can be achieved with functions in the Rsubread package [11]. We assume that an index of the mouse genome is already available - if not, this can be constructed from a FASTA file of the genome sequence with the buildindex command. In this example, we assume that the prefix for the index files is mm10. The reads in each FASTQ file are then aligned to the mouse genome, as shown below.

> library(Rsubread) > output.files <- sub(".fastq", ".bam", targets$FileName) > align("mm10", readfile1=targets$FileName, phredOffset=33, + input_format="FASTQ", output_file=output.files)

This produces a set of BAM files, where each file contains the read alignments for each library. The mapped reads can be counted into mouse genes by using the featureCounts function. It uses the exon intervals defined in the NCBI annotation of the mm10 genome.

> fc <- featureCounts(output.files, annot.inbuilt="mm10") > colnames(fc$counts) <- 1:12 > head(fc$counts)

1 2 3 4 5 6 7 8 9 10 11 12 497097 438 300 65 237 354 287 0 0 0 0 0 0 100503874 1 0 1 1 0 4 0 0 0 0 0 0 100038431 0 0 0 0 0 0 0 0 0 0 0 0 19888 1 1 0 0 0 0 10 3 10 2 0 0 20671 106 182 82 105 43 82 16 25 18 8 3 10 27395 309 234 337 300 290 270 560 464 489 328 307 342

The row names of the matrix represent the Entrez gene identiﬁers for each gene. In the output from featureCounts, the column names of fc$counts are the output ﬁle names from align. Here, we simplify them for brevity.

4.4.3 Count loading and annotation We create a DGEList object as follows

> group <- factor(paste0(targets$CellType, ".", targets$Status)) > y <- DGEList(fc$counts, group=group) > colnames(y) <- targets$GEO

Human-readable gene symbols can also be added to complement the Entrez identiﬁers for each gene, using the annotation in the org.Mm.eg.db package.

68 > require(org.Mm.eg.db) > y$genes <- select(org.Mm.eg.db,keys=rownames(y),columns="SYMBOL") > head(y$genes)

ENTREZID SYMBOL 1 497097 Xkr4 2 100503874 Gm19938 3 100038431 Gm10568 4 19888 Rp1 5 20671 Sox17 6 27395 Mrpl15

4.4.4 Filtering and normalization Here, a gene is only retained if it is expressed at a count-per-million (CPM) above 0.5 in at least two samples.

> keep <- rowSums(cpm(y) > 0.5) >= 2 > summary(keep)

Mode FALSE TRUE NA’s logical 11375 15804 0

> y <- y[keep, , keep.lib.sizes=FALSE]

TMM normalization is performed to eliminate composition biases between libraries.

> y <- calcNormFactors(y) > y$samples

group lib.size norm.factors GSM1480297 B.virgin 23218026 1.237 GSM1480298 B.virgin 21768136 1.214 GSM1480299 B.pregnant 24091588 1.126 GSM1480300 B.pregnant 22656713 1.070 GSM1480301 B.lactate 21522033 1.036 GSM1480302 B.lactate 20008326 1.087 GSM1480291 L.virgin 20384562 1.368 GSM1480292 L.virgin 21698793 1.365 GSM1480293 L.pregnant 22235847 1.005 GSM1480294 L.pregnant 21982745 0.923 GSM1480295 L.lactate 24719697 0.529 GSM1480296 L.lactate 24652963 0.535

69 The performance of the TMM normalization procedure can be examined using mean- difference (MD) plots. This visualizes the library size-adjusted log-fold change between two libraries (the difference) against the average log-expression across those libraries (the mean). The following MD plot is generated by comparing sample 1 against an artificial library constructed from the average of all other samples.

> plotMD(cpm(y, log=TRUE), column=1) > abline(h=0, col="red", lty=2, lwd=2)

Ideally, the bulk of genes should be centred at a log-fold change of zero. This indicates that any composition bias between libraries has been successfully removed. This quality check should be repeated by constructing a MD plot for each sample.

4.4.5 Data exploration The data can be explored by generating multi-dimensional scaling (MDS) plots. This visualizes the differences between the expression profiles of different samples in two dimensions.

> points <- c(0,1,2,15,16,17) > colors <- rep(c("blue", "darkgreen", "red"), 2) > plotMDS(y, col=colors[group], pch=points[group]) > legend("topleft", legend=levels(group), pch=points, col=colors, ncol=2)

70 Replicate samples from the same group cluster together in the plot, while samples from different groups form separate clusters. This indicates that the differences between groups are larger than those within groups, i.e., differential expression is greater than the variance and can be detected. The distance between basal samples on the left and luminal cells on the right is about 6 units, corresponding to a leading fold change of about 64-fold (26 = 64) between basal and luminal. The expression differences between virgin, pregnant and lactating are greater for luminal cells than for basal.

4.4.6 The design matrix The experimental design for this study can be parametrized with a one-way layout, whereby one coeﬃcient is assigned to each group. The design matrix contains the predictors for each sample and and is constructed using the code below.

> design <- model.matrix(~ 0 + group) > colnames(design) <- levels(group) > design

B.lactate B.pregnant B.virgin L.lactate L.pregnant L.virgin 1 0 0 1 0 0 0 2 0 0 1 0 0 0 3 0 1 0 0 0 0 4 0 1 0 0 0 0 5 1 0 0 0 0 0 6 1 0 0 0 0 0 7 0 0 0 0 0 1

71 8 0 0 0 0 0 1 9 0 0 0 0 1 0 10 0 0 0 0 1 0 11 0 0 0 1 0 0 12 0 0 0 1 0 0 attr(,"assign") [1] 1 1 1 1 1 1 attr(,"contrasts") attr(,"contrasts")$group [1] "contr.treatment"

4.4.7 Estimating the dispersion The NB dispersion is estimated using the estimateDisp function. This returns the DGEList object with additional entries for the estimated NB dispersions for all gene. These estimates can be visualized with plotBCV, which shows the root-estimate, i.e., the biological coeﬃcient of variation for each gene.

> y <- estimateDisp(y, design, robust=TRUE) > y$common.dispersion

[1] 0.0134

> plotBCV(y)

72 Note that only the trended dispersion is used under the quasi-likelihood (QL) pipeline. The tagwise and common estimates are shown here but will not be used further. For the QL dispersions, estimation can be performed using the glmQLFit function. This returns a DGEGLM object containing the estimated values of the GLM coeﬃcients for each gene, as well as the ﬁtted mean-QL dispersion trend, the squeezed QL estimates and the prior degrees of freedom (df). These can be visualized with the plotQLDisp function.

> fit <- glmQLFit(y, design, robust=TRUE) > head(fit$coefficients)

B.lactate B.pregnant B.virgin L.lactate L.pregnant L.virgin 497097 -11.14 -12.02 -11.23 -19.0 -19.03 -19.0 20671 -12.77 -12.51 -12.15 -14.5 -14.31 -14.1 27395 -11.27 -11.30 -11.53 -10.6 -10.87 -10.9 18777 -10.15 -10.21 -10.77 -10.1 -10.39 -10.4 21399 -9.89 -9.74 -9.79 -10.2 -9.97 -10.0 58175 -16.16 -14.85 -15.99 -13.3 -12.29 -12.1

> plotQLDisp(fit)

Setting robust=TRUE in glmQLFit is strongly recommended [21]. Setting robust=TRUE in estimateDisp has no eﬀect on the downstream analysis, but is nevertheless very useful as it identiﬁes genes that are outliers from the mean-NB dispersion trend.

73 4.4.8 Differential expression We test for significant differential expression in each gene, using the QL F-test. The contrast of interest can be specified using the makeContrasts function. Here, genes are tested for DE between the basal pregnant and lactating groups. This is done by defining the null hypothesis as B.pregnant - B.lactate = 0.

> con <- makeContrasts(B.pregnant - B.lactate, levels=design) > qlf <- glmQLFTest(fit, contrast=con)

The top set of most signiﬁcant genes can be examined with topTags. Here, a positive log-fold change represents genes that are up in B.pregnant over B.lactate. Multiplicity correction is performed by applying the Benjamini-Hochberg method on the p-values, to control the false discovery rate (FDR).

> topTags(qlf)

Coefficient: -1*B.lactate 1*B.pregnant ENTREZID SYMBOL logFC logCPM F PValue FDR 18071 12992 Csn1s2b -6.09 10.18 421 4.86e-11 7.67e-07 22881 211577 Mrgprf -5.15 2.74 345 1.30e-10 8.05e-07 12177 226101 Myof -2.32 6.44 322 1.97e-10 8.05e-07 851 381290 Atp2b4 -2.14 6.14 320 2.04e-10 8.05e-07 9279 140474 Muc4 7.17 6.05 308 2.64e-10 8.34e-07 18829 231830 Micall2 2.25 5.18 282 4.47e-10 1.18e-06 2491 24117 Wif1 1.82 6.76 260 7.30e-10 1.65e-06 18684 12740 Cldn4 5.32 9.87 298 8.88e-10 1.71e-06 22829 21953 Tnni2 -5.75 3.86 313 9.76e-10 1.71e-06 19483 231991 Creb5 -2.57 4.87 241 1.16e-09 1.83e-06

The top gene Csn1s2b has a large negative log2-fold-change, showing that it is far more highly expressed in lactating than pregnant mice. This gene is known to be a major source of protein in milk. The total number of DE genes in each direction at a FDR of 5% can be examined with decideTestsDGE. There are in fact nearly 4500 DE genes an FDR cut-oﬀ of 5% in this comparison:

> is.de <- decideTestsDGE(qlf, p.value=0.05) > summary(is.de)

[,1] -1 2505 0 10529 1 2770

74 The diﬀerential expression test results can be visualized using a smear plot. The log-fold change for each gene is plotted against the average abundance, i.e., logCPM in the result table above. Signiﬁcantly DE genes at a FDR of 5% are highlighted in red.

> plotSmear(qlf, de.tags=rownames(qlf)[is.de!=0])

We use glmTreat to narrow down the list of DE genes and focus on genes that are more biologically meaningful. We test whether the diﬀerential expression is signiﬁcantly above a log2-fold-change of log2 1.2, i.e., a fold-change of 1.2.

> tr <- glmTreat(fit, contrast=con, lfc=log2(1.2)) > topTags(tr)

Coefficient: -1*B.lactate 1*B.pregnant ENTREZID SYMBOL logFC unshrunk.logFC logCPM PValue FDR 18071 12992 Csn1s2b -6.09 -6.09 10.18 5.08e-11 8.02e-07 22881 211577 Mrgprf -5.15 -5.15 2.74 1.38e-10 9.13e-07 12177 226101 Myof -2.32 -2.32 6.44 2.66e-10 9.13e-07 851 381290 Atp2b4 -2.14 -2.14 6.14 2.89e-10 9.13e-07 9279 140474 Muc4 7.17 7.34 6.05 2.89e-10 9.13e-07 18829 231830 Micall2 2.25 2.25 5.18 6.15e-10 1.62e-06 18684 12740 Cldn4 5.32 5.32 9.87 9.30e-10 2.00e-06 22829 21953 Tnni2 -5.75 -5.76 3.86 1.01e-09 2.00e-06 2491 24117 Wif1 1.82 1.82 6.76 1.18e-09 2.08e-06 19483 231991 Creb5 -2.57 -2.57 4.87 1.47e-09 2.32e-06

75 Around 3000 genes are detected as DE with fold-change signiﬁcantly above 1.2 at an FDR cut-oﬀ of 5%.

> is.de <- decideTestsDGE(tr, p.value=0.05) > summary(is.de)

[,1] -1 1291 0 12827 1 1686

The test results are visualized in the following smear plot. Genes that are signiﬁcantly DE above a fold-change of 1.2 at an FDR of 5% are highlighted in red.

> plotSmear(tr, de.tags=rownames(tr)[is.de!=0])

4.4.9 ANOVA-like testing The diﬀerential expression analysis of two-group comparison can be easily extended to comparisons between three or more groups. This is done by creating a matrix of contrasts, where which each column represents a contrast between two groups of interest. In this manner, users can perform a one-way analysis of variance (ANOVA) for each gene. As an example, suppose we want to compare the three groups in the luminal population, i.e., virgin, pregnant and lactating. An appropriate contrast matrix can be created as shown below, to make pairwise comparisons between all three groups.

76 > con <- makeContrasts( + L.PvsL = L.pregnant - L.lactate, + L.VvsL = L.virgin - L.lactate, + L.VvsP = L.virgin - L.pregnant, levels=design)

The QL F-test is then applied to identify genes that are DE among the three groups. This combines the three pairwise comparisons into a single F-statistic and p-value. The top set of signiﬁcant genes can be displayed with topTags.

> anov <- glmQLFTest(fit, contrast=con) > topTags(anov)

Coefficient: LR test of 2 contrasts ENTREZID SYMBOL logFC.L.PvsL logFC.L.VvsL logCPM F PValue FDR 19230 19242 Ptn -1.54 7.26 7.97 2387 3.77e-17 5.96e-13 15679 13645 Egf -5.36 -7.22 3.67 1126 4.46e-15 3.22e-11 21207 52150 Kcnk6 -2.42 -7.00 5.91 1020 8.40e-15 3.22e-11 23907 15439 Hp 1.08 5.42 4.93 992 1.00e-14 3.22e-11 18071 12992 Csn1s2b -8.55 -11.36 10.18 1050 1.03e-14 3.22e-11 22626 14183 Fgfr2 -1.15 3.95 7.38 953 1.29e-14 3.22e-11 2901 20856 Stc2 -1.81 3.19 6.10 917 1.64e-14 3.22e-11 20062 11941 Atp2b2 -7.37 -10.56 6.60 1133 1.79e-14 3.22e-11 9083 13358 Slc25a1 -4.13 -4.91 7.49 888 2.01e-14 3.22e-11 8278 17068 Ly6d 3.42 9.24 4.68 886 2.04e-14 3.22e-11

Note that the three contrasts of pairwise comparisons are linearly dependent. Construct- ing the contrast matrix with any two of the contrasts would be suﬃcient to specify an ANOVA test. For instance, the contrast matrix shown below produces the same test results but with a diﬀerent column of log-fold changes.

> con <- makeContrasts( + L.PvsL = L.pregnant - L.lactate, + L.VvsP = L.virgin - L.pregnant, levels=design)

If all three contrasts are present in the contrast matrix, then only the log-fold changes of the ﬁrst two contrasts are shown in the output of topTags.

4.4.10 Gene ontology analysis Further analyses are required to interpret the diﬀerential expression results in a biological context. One common downstream procedure is a gene ontology (GO) enrichment analysis. Suppose we want to identify GO terms that are over-represented in the basal lactating group compared to the basal pregnancy group. This can be achieved by applying the goana function to the diﬀerential expression results of that comparison. The top set of most enriched GO terms can be viewed with the topGO function.

77 > con <- makeContrasts(B.lactate - B.pregnant, levels=design) > qlf <- glmQLFTest(fit, contrast=con) > go <- goana(qlf, species = "Mm") > topGO(go, n=30)

Term Ont N Up Down P.Up P.Down GO:0044822 poly(A) RNA binding MF 1092 107 394 1.000 3.44e-53 GO:0003723 RNA binding MF 1429 155 469 1.000 4.29e-50 GO:0042254 ribosome biogenesis BP 223 7 127 1.000 1.13e-40 GO:0022613 ribonucleoprotein complex biogenesis BP 336 24 161 1.000 1.58e-38 GO:0022626 cytosolic ribosome CC 97 1 75 1.000 4.19e-38 GO:0030529 intracellular ribonucleoprotein complex CC 646 43 246 1.000 3.87e-37 GO:1990904 ribonucleoprotein complex CC 646 43 246 1.000 3.87e-37 GO:0005730 nucleolus CC 663 79 239 1.000 9.61e-32 GO:0003676 nucleic acid binding MF 2834 423 712 0.998 1.42e-30 GO:0006364 rRNA processing BP 146 3 85 1.000 1.57e-28 GO:0016072 rRNA metabolic process BP 149 5 85 1.000 1.17e-27 GO:0031974 membrane-enclosed lumen CC 2850 409 698 1.000 2.62e-26 GO:0070013 intracellular organelle lumen CC 2793 401 684 1.000 1.11e-25 GO:0005840 ribosome CC 203 4 100 1.000 1.71e-25 GO:0043233 organelle lumen CC 2797 402 684 1.000 1.72e-25 GO:0044391 ribosomal subunit CC 157 1 84 1.000 9.64e-25 GO:0022625 cytosolic large ribosomal subunit CC 52 0 43 1.000 1.49e-24 GO:0031981 nuclear lumen CC 2558 384 631 0.996 2.88e-24 GO:1901363 heterocyclic compound binding MF 4346 668 975 0.998 8.95e-24 GO:0044445 cytosolic part CC 189 17 93 0.999 9.45e-24 GO:0032991 macromolecular complex CC 3900 584 890 1.000 1.26e-23 GO:0097159 organic cyclic compound binding MF 4393 676 980 0.998 5.15e-23 GO:0044446 intracellular organelle part CC 5362 874 1158 0.871 7.88e-23 GO:0044428 nuclear part CC 2955 452 700 0.992 4.74e-22 GO:0003735 structural constituent of ribosome MF 190 8 90 1.000 1.43e-21 GO:0044422 organelle part CC 5508 909 1176 0.740 3.05e-21 GO:0006396 RNA processing BP 672 57 215 1.000 5.97e-21 GO:0005634 nucleus CC 5357 881 1145 0.780 1.35e-20 GO:0034660 ncRNA metabolic process BP 353 24 133 1.000 6.45e-20 GO:0034470 ncRNA processing BP 269 14 110 1.000 8.47e-20

The row names of the output are the universal identifiers of the GO terms, with one term per row. The Term column gives the names of the GO terms. These terms cover three domains - biological process (BP), cellular component (CC) and molecular function (MF), as shown in the Ont column. The N column represents the total number of genes that are annotated with each GO term. The Up and Down columns represent the number of genes with the GO term that are significantly up- and down-regulated in this differential expression comparison, respectively. The P.Up and P.Down columns contain the p-values for over-representation of the GO term across the set of up- and down-regulated genes, respectively. The output table is sorted by the minimum of P.Up and P.Down by default. The goana function uses the NCBI RefSeq annotation. Therefore, the Entrez Gene iden-

78 tiﬁer (ID) should be supplied for each gene as the row names of qlf.

4.4.11 Gene set testing Another downstream step uses the rotation gene set test (ROAST) [33]. Given a set of genes, we can test whether the majority of the genes in the set are DE across the contrast of interest. It is useful when the speciﬁed set contains all genes involved in some pathway or process. In our case study, suppose we are interested in three GO terms related to cytokinesis. Each term will be used to deﬁne a set containing all genes that are annotated with that term. The names of these terms can be viewed as shown below.

> library(GO.db) > cyt.go <- c("GO:0032465", "GO:0000281", "GO:0000920") > term <- select(GO.db, keys=cyt.go, columns="TERM") > term

GOID TERM 1 GO:0032465 regulation of cytokinesis 2 GO:0000281 mitotic cytokinesis 3 GO:0000920 cell separation after cytokinesis

We construct a list of three components, each of which is a vector of Entrez Gene IDs for all genes annotated with one of the GO terms. We then convert the Gene IDs into row indices of the fit object using the function ids2indices.

> Rkeys(org.Mm.egGO2ALLEGS) <- cyt.go > ind <- ids2indices(as.list(org.Mm.egGO2ALLEGS), fit$genes$ENTREZID)

We proceed to run ROAST on the deﬁned gene sets for the contrast of interest. Suppose the comparison of interest is between the virgin and lactating groups in the basal population. We use fry to test for multiple gene sets.

> con <- makeContrasts(B.virgin-B.lactate, levels=design) > fr <- fry(y, index=ind, design=design, contrast=con) > fr

NGenes Direction PValue FDR PValue.Mixed FDR.Mixed GO:0032465 48 Up 0.000471 0.00141 3.72e-06 6.96e-06 GO:0000920 16 Down 0.001839 0.00276 4.64e-06 6.96e-06 GO:0000281 30 Up 0.007394 0.00739 2.50e-05 2.50e-05

Each row corresponds to a single gene set, i.e., GO term. The NGenes column gives the number of genes in each set. The net direction of change is determined from the signiﬁcance

79 of changes in each direction, and is shown in the Direction column. The PValue provides evidence for whether the majority of genes in the set are DE in the specified direction, whereas the PValue.Mixed tests for differential expression in any direction. FDRs are computed from the corresponding p-values across all sets. A barcode plot can be produced with the barcodeplot function to visualize the results for any particular set. In this case, visualization is performed for the gene set defined by GO:0032465. Here, genes are represented by bars and are ranked from left to right by decreasing log-fold change. This forms the barcode-like pattern. The line above the barcode shows the relative local enrichment of the vertical bars in each part of the plot. This particular plot suggests that most genes in this set are up-regulated in the virgin group compared to the lactating group.

> res <- glmQLFTest(fit, contrast=con) > barcodeplot(res$table$logFC, ind[[1]], main=names(ind)[1])

4.4.12 Setup This analysis was conducted on:

> sessionInfo()

80 [5] LC_TIME=English_Australia.1252 attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets methods base other attached packages: [1] GO.db_3.3.0 org.Mm.eg.db_3.3.0 tweeDEseqCountData_1.9.0 [4] NBPSeq_0.3.0 org.Hs.eg.db_3.3.0 RSQLite_1.0.0 [7] DBI_0.3.1 AnnotationDbi_1.33.11 IRanges_2.5.46 [10] S4Vectors_0.9.51 Biobase_2.31.3 BiocGenerics_0.17.5 [13] edgeR_3.13.9 limma_3.27.19 loaded via a namespace (and not attached): [1] Rcpp_0.12.4.5 magrittr_1.5 splines_3.3.0 munsell_0.4.3 statmod_1.4.24 [6] colorspace_1.2-6 lattice_0.20-33 stringr_1.0.0 plyr_1.8.3 tools_3.3.0 [11] grid_3.3.0 gtable_0.2.0 reshape2_1.4.1 ggplot2_2.1.0 qvalue_2.3.2 [16] stringi_1.0-1 scales_0.4.0 locfit_1.5-9.1

4.5 Diﬀerential splicing after Pasilla knockdown

4.5.1 Introduction The RNA-Seq data of this case study was produced by Brooks et al [3]. Drosophila melanogaster was used as a model system to study the proteins NOVA1 and NOVA2 which are known to regulate splicing in mammals. In particular, an RNA interference system (RNAi) was used to knock down the expression of the D. melanogaster ortholog of NOVA1 and NOVA2, which is Pasilla. The experiment compared treated and untreated cells from the S2-DRSC cell line. In this case study we are interested in exons and genes that are diﬀerentially expressed after Pasilla knockdown, as well as genes that are diﬀerentially spliced in the knockdown samples as compared to wildtype.

4.5.2 RNA-Seq samples The RNA-Seq data of the six samples were deposited on GEO http://www.ncbi.nlm.nih. gov/geo. The GEO accession numbers and titles were prepared in a csv ﬁle:

> library(edgeR) > GEO <- readTargets("GEO-samples.csv", sep=",") > GEO

GEO Title Pasilla 1 GSM461176 S2_DRSC_Untreated-1 Normal

81 2 GSM461177 S2_DRSC_Untreated-3 Normal 3 GSM461178 S2_DRSC_Untreated-4 Normal 4 GSM461179 S2_DRSC_CG8144_RNAi-1 Down 5 GSM461180 S2_DRSC_CG8144_RNAi-3 Down 6 GSM461181 S2_DRSC_CG8144_RNAi-4 Down

There are three untreated biological samples, in which Pasilla should be expressed at normal levels, and three treated biological samples, in which Pasilla should be expressed at reduced levels. While GEO records the sample information, the sequencing data ﬁle are actually held on the NCBI Short Read Archive (SRA). The RNA samples were sequenced on an Illumina Genome Analyzer II. Multiple sequencing runs were used for several of the samples, resulting in a total of 20 SRA ﬁles:

> SRA <- readTargets("SRA-Files.csv", sep=",") > SRA

SRA GEO Title RunDate FlowCellID Type ReadLength 1 SRR031708 GSM461176 S2_DRSC_Untreated-1 7/15/08 308T2AAXX SE 45 2 SRR031709 GSM461176 S2_DRSC_Untreated-1 7/15/08 308T2AAXX SE 45 3 SRR031710 GSM461176 S2_DRSC_Untreated-1 8/15/08 30AYWAAXX SE 45 4 SRR031711 GSM461176 S2_DRSC_Untreated-1 8/15/08 30AYWAAXX SE 45 5 SRR031712 GSM461176 S2_DRSC_Untreated-1 8/15/08 30AYWAAXX SE 45 6 SRR031713 GSM461176 S2_DRSC_Untreated-1 8/15/08 30AYWAAXX SE 45 7 SRR031714 GSM461177 S2_DRSC_Untreated-3 11/14/08 30MNEAAXX PE 37 8 SRR031715 GSM461177 S2_DRSC_Untreated-3 12/23/08 30M2BAAXX PE 37 9 SRR031716 GSM461178 S2_DRSC_Untreated-4 12/23/08 30M2BAAXX PE 37 10 SRR031717 GSM461178 S2_DRSC_Untreated-4 12/23/08 30M2BAAXX PE 37 11 SRR031718 GSM461179 S2_DRSC_CG8144_RNAi-1 7/15/08 308T2AAXX SE 45 12 SRR031719 GSM461179 S2_DRSC_CG8144_RNAi-1 7/18/08 308UEAAXX SE 45 13 SRR031720 GSM461179 S2_DRSC_CG8144_RNAi-1 8/15/08 30AYWAAXX SE 45 14 SRR031721 GSM461179 S2_DRSC_CG8144_RNAi-1 8/15/08 30AYWAAXX SE 45 15 SRR031722 GSM461179 S2_DRSC_CG8144_RNAi-1 8/15/08 30AYWAAXX SE 45 16 SRR031723 GSM461179 S2_DRSC_CG8144_RNAi-1 8/21/08 308A0AAXX SE 45 17 SRR031724 GSM461180 S2_DRSC_CG8144_RNAi-3 12/23/08 30M2BAAXX PE 37 18 SRR031725 GSM461180 S2_DRSC_CG8144_RNAi-3 12/23/08 30M2BAAXX PE 37 19 SRR031726 GSM461181 S2_DRSC_CG8144_RNAi-4 12/23/08 30M2BAAXX PE 37 20 SRR031727 GSM461181 S2_DRSC_CG8144_RNAi-4 12/23/08 30M2BAAXX PE 37

The last two columns of the above target ﬁle indicate whether the samples are single end (SE) sequencing with 45 base-pair reads or paired end (PE) sequencing with 37 bp reads.

4.5.3 Read alignment and processing The SRA format files were first converted to FASTQ format using the SRA Toolkit. Then an index file of the D. melanogaster reference genome was built in Rsubread[11] using the FASTA

82 files downloaded from ftp://ftp.ncbi.nlm.nih.gov/genomes/Drosophila_melanogaster/RELEASE_ 5_48. Finally, reads were aligned to the reference D. melanogaster genome using Rsubread. Next we counted the number of reads or fragments overlapping each annotated exon of each gene. GFF files containing gene and exon annotation were downloaded from ftp: //ftp.ncbi.nlm.nih.gov/genomes/Drosophila_melanogaster/RELEASE_5_48. The five *.gff files, one for each chromosome, were concatenated into one file, and repeated exons instances of the same exon (same start and stop position) were removed to create a data frame of start/stop positions called unique.gff. The single end (SE) reads were counted by:

> fc_SE <- featureCounts(SE_bam_files, annot.ext="unique.gff", + isGTFAnnotationFile=TRUE, GTF.featureType="exon", GTF.attrType="ID", + useMetaFeatures=FALSE, allowMultiOverlap=TRUE) where SE bam files is a vector of BAM ﬁle names for the SE reads. The paired end (PE) reads were counted by:

> fc_PE <- featureCounts(PE_bam_files, annot.ext="unique.gff", + isGTFAnnotationFile=TRUE, GTF.featureType="exon", GTF.attrType="ID", + useMetaFeatures=FALSE, allowMultiOverlap=TRUE, isPairedEnd=TRUE) where PE bam files is a vector of BAM ﬁle names for the PE reads.

4.5.4 Count loading and annotation We create a DGEList object as follows

> y.all <- DGEList(counts=cbind(fc_SE$counts, fc_PE$counts), genes=fc_SE$annotation) > dim(y.all)

[1] 74184 20

> head(y.all$genes)

GeneID Chr Start End Strand Length 138088 30970 NC_004354.3 138094 139379 - 1286 138087 30970 NC_004354.3 139445 139611 - 167 138089 30970 NC_004354.3 139445 139889 - 445 138086 30970 NC_004354.3 139713 139889 - 177 138091 30971 NC_004354.3 140011 141629 + 1619 138092 30971 NC_004354.3 142415 144271 + 1857

The annotation includes Entrez ID and the length, chromosome and start and stop position of each exon. We resort the samples back to original SRA order and collapse the data so that there is a single column for each GEO sample by summing the counts over the technical replicates:

83 > y.all <- y.all[, SRA$SRA] > y <- sumTechReps(y.all, ID=SRA$GEO) > y$samples

group lib.size norm.factors GSM461176 1 31007529 1 GSM461177 1 13040952 1 GSM461178 1 15030819 1 GSM461179 1 28143539 1 GSM461180 1 14901292 1 GSM461181 1 16264066 1

> colnames(y) <- c("N1","N3","N4","D1","D3","D4")

Annotation for D. melanogaster genes was downloaded from ftp://ftp.ncbi.nlm.nih. gov/gene/DATA/GENE_INFO/Invertebrates. We now add selected annotation columns to the DGEList object:

> ncbi.L1 <- readLines("Drosophila_melanogaster.gene_info", n = 1) > ncbi.colname <- unlist(strsplit(substring(ncbi.L1, 10, 234), ’ ’)) > ncbi <- read.delim("Drosophila_melanogaster.gene_info", skip=1, + header=FALSE, stringsAsFactors=FALSE) > colnames(ncbi) <- ncbi.colname > m <- match(y$genes$GeneID, ncbi$GeneID) > y$genes$Chr <- ncbi$chromosome[m] > y$genes$Symbol <- ncbi$Symbol[m] > y$genes$Strand <- NULL > head(y$genes)

GeneID Chr Start End Length Symbol 138088 30970 X 138094 139379 1286 CG3038 138087 30970 X 139445 139611 167 CG3038 138089 30970 X 139445 139889 445 CG3038 138086 30970 X 139713 139889 177 CG3038 138091 30971 X 140011 141629 1619 G9a 138092 30971 X 142415 144271 1857 G9a

4.5.5 Filtering and normalization Here, an exon is only retained if it is expressed at a count-per-million (CPM) above 1 in at least 3 samples.

> keep <- rowSums(cpm(y) > 1) >=3 > summary(keep)

84 Mode FALSE TRUE NA’s logical 36926 37258 0

> y <- y[keep, , keep.lib.sizes=FALSE]

TMM normalization is performed to eliminate composition biases between libraries.

> y <- calcNormFactors(y) > y$samples

group lib.size norm.factors N1 1 30872843 0.955 N3 1 12962245 1.031 N4 1 14908555 0.976 D1 1 27989806 1.005 D3 1 14760887 1.022 D4 1 16172265 1.014

4.5.6 Data exploration The data can be explored by generating multi-dimensional scaling (MDS) plots. This visualizes the differences between the expression profiles of different samples in two dimensions.

> plotMDS(y)

The MDS plot shows clear separation of the Pasilla down vs normal samples, but also a batch eﬀect associated with sequencing type and date.

85 4.5.7 The design matrix To account for the batch eﬀect observed from the MDS plot, we create a design matrix as follows:

> Batch <- factor(c(1,3,4,1,3,4)) > Pasilla <- factor(GEO$Pasilla, levels=c("Normal","Down")) > design <- model.matrix(~ Batch + Pasilla) > design

(Intercept) Batch3 Batch4 PasillaDown 1 1 0 0 0 2 1 1 0 0 3 1 0 1 0 4 1 0 0 1 5 1 1 0 1 6 1 0 1 1 attr(,"assign") [1] 0 1 1 2 attr(,"contrasts") attr(,"contrasts")$Batch [1] "contr.treatment" attr(,"contrasts")$Pasilla [1] "contr.treatment"

4.5.8 Estimating the dispersion We estimate NB dispersions using the estimateDisp function. The estimated dispersions can be visualized with plotBCV.

> y <- estimateDisp(y, design, robust=TRUE) > y$common.dispersion

[1] 0.0141

> plotBCV(y)

86 Note that only the trended dispersion is used under the quasi-likelihood (QL) pipeline. The tagwise and common estimates are shown here but will not be used further. For the QL dispersions, estimation can be performed using the glmQLFit function. The results can be visualized with the plotQLDisp function.

> fit <- glmQLFit(y, design, robust=TRUE) > plotQLDisp(fit)

87 4.5.9 Diﬀerential expression We test for diﬀerentially expressed exons between Pasilla knockdown and normal using the QL F-test.

> qlf <- glmQLFTest(fit, coef=4)

The top set of most signiﬁcant exons can be examined with topTags. Here, a positive log-fold change represents exons that are up in Pasilla knockdown over normal. Multiplicity correction is performed by applying the Benjamini-Hochberg method on the p-values, to control the false discovery rate (FDR).

> topTags(qlf)

Coefficient: PasillaDown GeneID Chr Start End Length Symbol logFC logCPM F PValue FDR 150709 32007 X 10674926 10676128 1203 sesB -3.26 7.21 949 7.41e-15 1.39e-10 150713 32007 X 10675026 10676128 1103 sesB -3.26 7.21 948 7.46e-15 1.39e-10 150697 32008 X 10672987 10673728 742 Ant2 2.85 6.14 863 1.48e-14 1.84e-10 91614 42865 3R 19970915 19971592 678 Kal1 -4.43 3.81 756 3.88e-14 3.61e-10 107856 44030 3L 2561932 2562843 912 msn -2.46 5.59 615 1.74e-13 1.30e-09 150702 32008 X 10674230 10674694 465 Ant2 2.97 4.55 575 2.83e-13 1.33e-09 150695 32008 X 10674230 10674559 330 Ant2 2.96 4.55 574 2.86e-13 1.33e-09 70750 44258 3R 5271691 5272628 938 ps -2.27 5.95 572 2.97e-13 1.33e-09 11333 44548 2R 6407125 6408782 1658 lola 2.26 6.15 565 3.21e-13 1.33e-09 96433 43230 3R 22697648 22697717 70 BM-40-SPARC -2.17 6.65 542 4.37e-13 1.63e-09

The total number of DE exons in each direction at a FDR of 5% can be examined with decideTestsDGE.

> is.de <- decideTestsDGE(qlf, p.value=0.05) > summary(is.de)

[,1] -1 2059 0 33385 1 1814

4.5.10 Alternative splicing We detect alternative splicing by testing for diﬀerential exon usage between Pasilla knockdown and normal in each gene.

88 > sp <- diffSpliceDGE(fit, coef=4, geneid="GeneID", exonid="Start")

Total number of exons: 37258 Total number of genes: 8192 Number of genes with 1 exon: 1619 Mean number of exons in a gene: 5 Max number of exons in a gene: 56

Two testing methods at the gene-level are provided. The Simes’ method is likely to be more powerful when only a minority of the exons for a gene are diﬀerentially spliced. The F-tests are likely to be powerful for genes in which several exons are diﬀerentially spliced. The top spliced genes under the Simes’ method are shown below:

> topSpliceDGE(sp, test="Simes", n=20)

GeneID Chr Symbol NExons P.Value FDR 141235 45320 X trol 44 1.64e-30 1.08e-26 11214 44548 2R lola 30 4.28e-30 1.41e-26 95956 44448 3R scrib 35 1.10e-20 2.40e-17 107810 44030 3L msn 24 1.15e-18 1.89e-15 19880 36773 2R Dg 15 2.17e-18 2.86e-15 16060 36542 2R shot 38 2.03e-17 2.22e-14 82117 42130 3R osa 17 2.50e-17 2.35e-14 32242 37893 2R slik 19 2.59e-15 2.13e-12 131170 40205 3L CG42674 16 3.88e-15 2.84e-12 163416 32817 X CrebB-17A 12 1.00e-14 6.58e-12 150694 32008 X Ant2 5 1.02e-13 6.07e-11 110493 38491 3L ens 16 1.88e-13 1.03e-10 41795 3771968 2L Msp-300 33 2.80e-12 1.41e-09 115767 38879 3L pbl 12 3.84e-12 1.80e-09 2032 2768716 2R mim 25 8.98e-12 3.93e-09 526 35494 2R laccase2 9 2.81e-11 1.11e-08 150710 32007 X sesB 7 2.88e-11 1.11e-08 166094 33098 X CG32521 8 4.29e-11 1.57e-08 52823 34652 2L vir-1 7 8.31e-11 2.88e-08 85970 42428 3R Stat92E 14 4.41e-10 1.45e-07

The top spliced genes identiﬁed by F-tests are shown below:

> topSpliceDGE(sp, test="gene", n=20)

GeneID Chr Symbol NExons gene.F P.Value FDR 141235 45320 X trol 44 52.5 2.53e-51 1.66e-47 11214 44548 2R lola 30 42.7 6.84e-34 2.25e-30 41795 3771968 2L Msp-300 33 22.7 2.34e-27 5.13e-24 95956 44448 3R scrib 35 17.2 1.08e-24 1.78e-21 16060 36542 2R shot 38 11.1 6.90e-20 9.07e-17

89 32242 37893 2R slik 19 25.8 1.22e-18 1.34e-15 166094 33098 X CG32521 8 64.1 1.14e-14 1.07e-11 19880 36773 2R Dg 15 21.8 2.57e-14 2.11e-11 2032 2768716 2R mim 25 10.7 8.49e-14 6.20e-11 107810 44030 3L msn 24 10.6 3.12e-13 2.05e-10 150694 32008 X Ant2 5 108.1 4.05e-13 2.36e-10 82117 42130 3R osa 17 15.6 4.30e-13 2.36e-10 163416 32817 X CrebB-17A 12 22.3 2.49e-12 1.26e-09 150710 32007 X sesB 7 51.5 5.26e-12 2.47e-09 131170 40205 3L CG42674 16 12.7 4.91e-11 2.15e-08 115767 38879 3L pbl 12 15.8 2.81e-10 1.16e-07 134207 40464 3L Ten-m 12 15.6 3.49e-10 1.35e-07 11103 36104 2R G-oalpha47A 13 14.1 3.87e-10 1.41e-07 108973 38376 3L BtbVII 10 18.7 5.84e-10 2.02e-07 110493 38491 3L ens 16 10.6 7.63e-10 2.51e-07

We plot all the exons for the top two most diﬀerentially spliced genes. Exons that are individually signiﬁcant are highlighted.

> par(mfrow=c(1,2)) > plotSpliceDGE(sp, geneid="trol", genecol="Symbol") > plotSpliceDGE(sp, geneid="lola", genecol="Symbol")

We can see that a block of five or six exons at the right end of the trol gene are relatively lost when Pasilla is down. Most exons in the first half of the gene behave similarly to each other. This gene is on the negative strand, so transcription is from right to left. The gene trol was identified by Brooks et al [3] to have a novel set of coordinately regulated exons.

90 4.5.11 Setup This analysis was conducted on:

> sessionInfo()

R version 3.3.0 beta (2016-04-14 r70486) Platform: x86_64-w64-mingw32/x64 (64-bit) Running under: Windows 7 x64 (build 7601) Service Pack 1 locale: [1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252 [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C [5] LC_TIME=English_Australia.1252 attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets methods base other attached packages: [1] GO.db_3.3.0 org.Mm.eg.db_3.3.0 tweeDEseqCountData_1.9.0 [4] NBPSeq_0.3.0 org.Hs.eg.db_3.3.0 RSQLite_1.0.0 [7] DBI_0.3.1 AnnotationDbi_1.33.11 IRanges_2.5.46 [10] S4Vectors_0.9.51 Biobase_2.31.3 BiocGenerics_0.17.5 [13] edgeR_3.13.9 limma_3.27.19 loaded via a namespace (and not attached): [1] Rcpp_0.12.4.5 magrittr_1.5 splines_3.3.0 munsell_0.4.3 statmod_1.4.24 [6] colorspace_1.2-6 lattice_0.20-33 stringr_1.0.0 plyr_1.8.3 tools_3.3.0 [11] grid_3.3.0 gtable_0.2.0 reshape2_1.4.1 ggplot2_2.1.0 qvalue_2.3.2 [16] stringi_1.0-1 scales_0.4.0 locfit_1.5-9.1

4.5.12 Acknowledgements Thanks to Yang Liao for mapping the reads and running featureCounts and Yifang Hu for the initial analysis of the data.

4.6 CRISPR-Cas9 knockout screen analysis

4.6.1 Introduction Dai et al. (2014) [7] describe the use of edgeR to analyze data from pooled genetic screens utilizing either shRNAs or CRISPR-Cas9 to disrupt gene expression in a population of cells. In this case study we analyze data from a pooled screen that uses CRISPR-Cas9 (clus- tered regularly interspaced short palindromic repeats-associated nuclease Cas9) knockout

91 technology. In this example, a library of around 64,000 sgRNAs (as used in Shalem et al. 2014 [29]) were screened to look for genes that may lead to resistance from a particular drug. This unpublished data set has been anonymised.

4.6.2 Sequence processing Multiple single guide RNAs (sgRNAs) per gene (generally between 3-6) were included in the screen. Below we read in the raw sequences from the paired end fastq files screen4 R1.fastq and screen4 R2.fastq using the processAmplicons function in edgeRThis˙ screen employed a dual indexing strategy where the first 8 bases from each pair of reads contained an index sequence that uniquely identifies which sample a particular sgRNA sequence originated from. Matches between sample indexes and sgRNAs listed in the files Samples4.txt and sgRNAs4.txt are identified by processAmplicons to produce a DGEList of counts.

> # Read in sample & sgRNA information > sampleanno <- read.table("Samples4.txt", header=TRUE, sep="\t") > sampleanno[1:5,] > sgseqs <- read.table("sgRNAs4.txt", header=TRUE, sep="\t") > sgseqs[1:5,] > # Process raw sequences from fastq files > x <- processAmplicons("screen4_R1.fastq", readfile2="screen4_R2.fastq", + barcodefile="Samples4.txt", hairpinfile="sgRNAs4.txt", + barcodeStart=1, barcodeEnd=8, hairpinStart=33, hairpinEnd=52, + barcodeStartRev=1, barcodeEndRev=8, verbose=TRUE)

Note that this dual indexing strategy requires an additional column named ‘Sequences- Rev’ in the file that contains the sample annotation information. Also, readFile2 must be specified, along with position information (barcodeStartRev, barcodeEndRev) for the second index in the second read from each pair (in this case the index can be found in the first 8 bases).

4.6.3 Filtering and data exploration We next ﬁlter out sgRNAs and samples with low numbers of reads.

> x

An object of class "DGEList" $counts A1_1_1 A2_1_2 A3_1_3 A4_1_4 A5_1_5 A6_1_6 A7_2_1 A8_2_2 A9_2_3 A10_2_4 A11_2_5 A12_2_6 sgRNA1 0 14 0 0 3 36 1 55 0 23 0 62 sgRNA2 0 18 0 0 1 22 0 26 0 29 0 43 sgRNA3 0 50 0 0 4 52 1 98 0 60 0 111

92 sgRNA4 0 32 0 0 3 55 2 54 0 51 0 57 sgRNA5 0 7 0 0 1 3 0 3 0 5 1 5 A13_3_1 A14_3_2 A15_3_3 A16_3_4 A17_3_5 A18_3_6 A19_4_1 A20_4_2 A21_4_3 A22_4_4 A23_4_5 sgRNA1 0 21 0 30 21 36 0 37 0 39 1 sgRNA2 0 27 0 27 26 30 1 23 0 44 0 sgRNA3 0 59 0 62 24 63 0 44 0 106 0 sgRNA4 0 43 0 50 19 26 0 44 0 94 0 sgRNA5 0 3 0 3 1 7 0 1 0 8 0 A24_4_6 B1_5_1 B2_5_2 B3_5_3 B4_5_4 B5_5_5 B6_5_6 B7_6_1 B8_6_2 B9_6_3 B10_6_4 B11_6_5 sgRNA1 63 3 5 5 26 11 4 3 4 14 3 8 sgRNA2 34 14 27 16 77 22 42 9 24 12 27 15 sgRNA3 70 16 39 27 53 41 43 31 24 14 35 43 sgRNA4 107 15 13 12 24 12 22 10 10 11 20 15 sgRNA5 3 0 5 12 15 6 25 6 9 6 3 9 B12_6_6 B13_7_1 B14_7_2 B15_7_3 B16_7_4 B17_7_5 B18_7_6 B19_8_1 B20_8_2 B21_8_3 B22_8_4 sgRNA1 6 9 10 6 8 11 31 6 13 9 25 sgRNA2 41 11 23 14 64 46 66 18 31 12 94 sgRNA3 45 38 51 14 59 38 73 31 29 31 63 sgRNA4 18 13 12 7 28 15 23 14 18 19 27 sgRNA5 16 1 5 0 3 7 11 1 7 3 18 B23_8_5 B24_8_6 A1_1_7 A2_1_8 A3_1_9 A7_2_7 A8_2_8 A9_2_9 A13_3_7 A14_3_8 A15_3_9 A19_4_7 sgRNA1 13 19 0 18 0 0 38 0 0 16 0 0 sgRNA2 36 64 0 12 0 0 18 0 0 15 0 0 sgRNA3 58 74 0 30 0 4 71 0 0 32 0 1 sgRNA4 19 36 0 27 0 1 39 0 0 34 0 1 sgRNA5 24 12 0 2 0 0 2 0 0 8 0 0 A20_4_8 A21_4_9 B1_5_7 B2_5_8 B3_5_9 B7_6_7 B8_6_8 B9_6_9 B13_7_7 B14_7_8 B15_7_9 B19_8_7 sgRNA1 32 0 5 6 5 10 5 15 2 9 3 10 sgRNA2 16 0 9 20 8 11 22 7 7 22 16 20 sgRNA3 39 0 10 19 23 19 14 30 30 35 24 27 sgRNA4 28 0 8 9 9 8 10 5 11 9 8 11 sgRNA5 0 0 0 9 4 4 10 3 2 2 0 3 B20_8_8 B21_8_9 sgRNA1 15 8 sgRNA2 20 9 sgRNA3 18 17 sgRNA4 12 11 sgRNA5 10 8 64746 more rows ...

$samples ID lib.size norm.factors SequencesReverse group Infection Replicate IndexF IndexR 1 A1_1_1 188 1 TAAGGCGA Drug 1 1 1 1 2 A2_1_2 667530 1 CGTACTAG NoDrug 1 1 1 2 3 A3_1_3 1340 1 AGGCAGAA Drug 1 1 1 3 4 A4_1_4 2473 1 TCCTGAGC NoDrug 1 1 1 4 5 A5_1_5 69161 1 GGACTCCT Drug 1 1 1 5 67 more rows ...

93 $genes ID Sequences Gene 1 sgRNA1 TACCCTGGGACTGTACCCCC 99 2 sgRNA2 ACCCTTGCTGCACGACCTGC 99 3 sgRNA3 TCGCTCGCCCCGCTCTTCCT 99 4 sgRNA4 TGACGCCTCGGACGTGTCTG 19 5 sgRNA5 CGTCATAGCCAATCTTCTTC 19 64746 more rows ...

> table(x$samples$group)

Drug NoDrug 40 32

> # Filter sgRNAs and samples with low counts > # Need a CPM greater than 5 in 15 or more samples to keep sgRNAs > selr <- rowSums(cpm(x$counts)>5)>=15 > # Need at least 100,000 reads to keep a given sample > selc <- colSums(x$counts)>=100000 > x <- x[selr,selc] > # Set up drug treatment colours > cols <- as.numeric(x$samples$group)+2 > # Plot number of sgRNAs that could be matched per sample > # and total for each sgRNA across all samples > par(mfrow=c(2,1)) > barplot(colSums(x$counts), las=2, main="Counts per index", col=cols, cex.names=0.5, cex.axis=0.8) > legend("topright", legend=c("Control", "Drug"), col=c(3,4), pch=15) > barplot(rowSums(x$counts), las=2, main="Counts per sgRNA", axisnames=FALSE, cex.axis=0.8)

94 A multidimensional scaling plot was generated to assess the consistency between replicate samples. There is a clear separation between the two infections, indicating the need to incorporate an eﬀect for this in the GLM.

> # Make an MDS plot to visualise relationships between replicate samples > # Set up infection colours > cols2 <- x$samples$Infection > par(mfrow=c(1,2)) > plotMDS(x, col=cols, main="MDS Plot: drug treatment colours") > legend("topleft", legend=c("Control", "Drug"), col=c(3,4), pch=15) > plotMDS(x, col=cols2, main="MDS Plot: infection colours") > legend("topleft", legend=c("Inf#1", "Inf#2"), col=c(1,2), pch=15)

4.6.4 The design matrix and dispersion estimation A design matrix is set up for the GLM analysis, and the sgRNA-speciﬁc variation is estimated and plotted (while taking into account both drug treatment and infection number).

> # Set up design matrix for GLM > treatment <- relevel(as.factor(x$samples$group), "NoDrug") > infection <- as.factor(x$samples$Infection) > des <- model.matrix(~treatment+infection) > des[1:5,]

95 (Intercept) treatmentDrug infection2 1 1 0 0 2 1 0 0 3 1 0 0 4 1 0 0 5 1 0 0

> colnames(des)[2:3] <- c("Drug", "Infection2") > # Estimate dispersions > xglm <- estimateDisp(x, des) > sqrt(xglm$common.disp)

[1] 0.258

> # Plot BCVs versus abundance > plotBCV(xglm, main="BCV Plot")

4.6.5 Differential representation analysis We use the function glmFit to fit the sgRNA-specific models and glmLRT to do the testing between the drug treated and control samples. The top ranked sgRNAs are listed using the topTags function and sgRNAs with FDR < 0.0001 [2] and log-fold-change ≥ 1 are highlighted on a plot of log-fold-change versus log-counts-per-millions by the plotSmear function. Since this is a positive screen, we highlight over-represented sgRNAs (i.e. those with positive log- fold-changes) since the model is parameterized to compare drug treatment versus control (coefficient 2 in the design matrix).

96 > # Fit negative bionomial GLM > fit <- glmFit(xglm, des) > # Carry out Likelihood ratio test > lrt <- glmLRT(fit, coef=2) > # Show top ranked sgRNAs > topTags(lrt)

Coefficient: Drug ID Sequences Gene logFC logCPM LR PValue FDR 816 sgRNA816 TCCGAACTCCCCCTTCCCGA 269 4.36 7.32 699 4.41e-154 2.49e-149 4070 sgRNA4070 GTTGTGCTCAGTACTGACTT 1252 2.94 8.00 659 2.11e-145 5.94e-141 6351 sgRNA6351 AAAAACGTATCTATTTTTAC 1957 3.37 6.34 422 8.43e-94 1.58e-89 12880 sgRNA12880 CTGCACCGAAGAGAGCTGCT 3979 2.83 7.04 322 5.38e-72 7.58e-68 23015 sgRNA23015 CAATTTGATCTCTTCTACTG 6714 3.16 4.83 233 1.34e-52 1.51e-48 62532 sgRNA62532 AAACACGTCCAGTGCAGCCC 19612 2.79 4.91 216 6.15e-49 5.78e-45 38819 sgRNA38819 TACGTTGTCGGGCGCCGCCA 11531 2.42 6.54 204 2.93e-46 2.36e-42 3887 sgRNA3887 AACGCTGGACTCGAATGGCC 1194 2.28 5.33 203 4.03e-46 2.84e-42 19299 sgRNA19299 GGGGTCTTACCCGAGGCTCC 5732 1.94 5.63 202 7.64e-46 4.78e-42 52924 sgRNA52924 CCACCGCGTTCCACTTCTTG 16395 2.87 6.64 193 5.49e-44 3.09e-40

> # Select sgRNAs with FDR < 0.0001 and logFC <= -1 to highlight on plot > thresh <- 0.0001 > lfc <- 1 > top4 <- topTags(lrt, n=Inf) > top4ids <- top4$table[top4$table$FDR=lfc,1] > # Plot logFC versus logCPM > plotSmear(lrt, de.tags=top4ids, pch=20, cex=0.6, main="Drug treatment vs Control") > abline(h = c(-1, 0, 1), col = c("dodgerblue", "yellow", "dodgerblue"), lty=2)

97 4.6.6 Gene set tests to summarize over multiple sgRNAs targeting the same gene We finish this analysis by summarising data across multiple sgRNAs that target the same gene in order to get a gene-by-gene ranking, rather than a sgRNA-specific one. The camera gene-set test [34] is used for this purpose. For this analysis, the collection of sgRNAs that target a specific gene can be regarded as a ‘set’. In the code below, we restrict our analysis to genes with more than 3 sgRNAs. A barcode plot, highlighting the rank of sgRNAs for a given gene relative to the entire data set is generated for the top-ranked gene (11531). Abundance of sgRNAs targeting this gene tend to increase with drug treatment (FDR=0.0003).

> # Carry out camera gene-set analysis > genesymbols <- x$genes[,3] > genesymbollist <- list() > unq <- unique(genesymbols) > unq <- unq[!is.na(unq)] > for(i in unq) { + sel <- genesymbols==i & !is.na(genesymbols) + if(sum(sel)>3) + genesymbollist[[i]] <- which(sel) + } > # Run camera for all genes > camera.res <- camera(xglm, index=genesymbollist, des, contrast=2) > # Display results for top ranked genes > camera.res[1:10,]

NGenes Correlation Direction PValue FDR 11531 4 -0.1744 Up 1.08e-07 0.00032 19612 5 -0.0324 Up 1.16e-07 0.00032 10784 4 -0.1885 Up 7.31e-07 0.00134 8808 4 -0.1059 Up 1.65e-06 0.00228 10386 4 -0.1050 Up 2.36e-05 0.02606 3979 4 -0.0121 Up 4.16e-05 0.03823 8493 4 -0.1267 Up 8.30e-05 0.06537 4635 5 -0.0959 Up 1.05e-04 0.07214 2005 4 -0.0240 Up 2.11e-04 0.12951 9860 5 -0.0996 Up 2.55e-04 0.14031

> # Make a barcode plot for an example that ranks highly > # Gene 11531 > barcodeplot(lrt$table$logFC,index=genesymbollist[[11531]], + main="Barcodeplot for Gene 11531", + labels=c("Positive logFC", "Negative logFC"), + quantile=c(-0.5,0.5))

98 The raw data from this example and several other case studies for this technology can be found at http://bioinf.wehi.edu.au/shRNAseq/.

4.6.7 Setup This analysis was conducted on:

> sessionInfo()

R version 3.3.0 beta (2016-04-14 r70486) Platform: x86_64-w64-mingw32/x64 (64-bit) Running under: Windows 7 x64 (build 7601) Service Pack 1 locale: [1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252 [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C [5] LC_TIME=English_Australia.1252 attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets methods base other attached packages: [1] GO.db_3.3.0 org.Mm.eg.db_3.3.0 tweeDEseqCountData_1.9.0 [4] NBPSeq_0.3.0 org.Hs.eg.db_3.3.0 RSQLite_1.0.0 [7] DBI_0.3.1 AnnotationDbi_1.33.11 IRanges_2.5.46 [10] S4Vectors_0.9.51 Biobase_2.31.3 BiocGenerics_0.17.5 [13] edgeR_3.13.9 limma_3.27.19 loaded via a namespace (and not attached): [1] Rcpp_0.12.4.5 magrittr_1.5 splines_3.3.0 munsell_0.4.3 statmod_1.4.24 [6] colorspace_1.2-6 lattice_0.20-33 stringr_1.0.0 plyr_1.8.3 tools_3.3.0

99 [11] grid_3.3.0 gtable_0.2.0 reshape2_1.4.1 ggplot2_2.1.0 qvalue_2.3.2 [16] stringi_1.0-1 scales_0.4.0 locfit_1.5-9.1

4.6.8 Acknowledgements Thanks to Dr Sam Wormald from the WEHI for providing the data set used in this case study.

100 Bibliography

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